摘要
根据地层特征曲线和围岩剪切滑移理论,分析围岩最小荷载计算方法。基于薄壁圆筒与锚杆端锚理论,分析喷射混凝土层(简称喷层)及锚杆的支护抗力确定方法。建立由锚杆支护抗力、喷层支护抗力和围岩荷载构成的圆形锚喷支护隧道结构功能函数。为了求解该非线性隐式功能函数的可靠度指标,首先,利用验算点与可靠度指标的关系,将极限状态方程由多自变量(结构基本变量)的隐式形式转变为单自变量(可靠度指标)的隐式形式;然后,通过泰勒公式将其展开成级数,截取其前若干项,导出可靠度指标的迭代逼近计算公式;再将复合函数求导法则与差分求导结合起来,推出逼近计算表达式中系数的导数求解格式。上述研究形成了基于泰勒级数与差分求导数结合的锚喷支护隧道结构稳定可靠度指标分析方法。采用该方法分析某公路隧道结构的稳定可靠度,并与蒙特卡罗方法的精确解进行对比,两者的绝对差异为0.018%,相对差异为4.47%。
A calculation method for minimal rock pressure was analyzed according to the ground characteristics curve and shear failure theory.Determination of support pressures with shotcrete lining and rockbolts was investigated using the thin-wall cylinder theory and the analysis of point anchored reinforcement.A performance function involving rock pressure as well as support pressure with rockbolts and shotcrete was proposed for a circular tunnel structure.To calculate the reliability index,the nonlinear implicit performance function of multiple arguments（basic random variables） was first transformed into an expression with a single argument（reliability index） by using the correlation between the check point and the reliability index,and then an iterative approximation algorithm was developed to calculate the reliability index by using a Taylor series expansion truncated up to the second order.Evaluation of derivatives for the coefficients in the expansion was performed through a difference scheme,using the chain rule for the derivatives of a compound function.Comparison was conducted between the proposed approach and the Monte-Carlo simulation method using a road tunnel as an example.The results show that the absolute error between the two values of probability of failure is 0.0018%,and the relative error is 4.47%.
出处
《土木工程学报》
EI
CSCD
北大核心
2011年第3期113-119,共7页
China Civil Engineering Journal
基金
国家自然科学基金(51078136
50808076)
湖南省自然科学基金(09JJ3113)
关键词
隧道工程
圆筒模型
喷锚衬砌
可靠度指标
泰勒级数
tunnel engineering
cylinder model
rockbolts and shotcrete support
reliability index
Taylor series
