隧道围岩塌落机理与锚杆支护结构的上限分析研究
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摘要
隧道稳定性问题是隧道工程中的基础性问题之一,如何在支护条件已知情况下对隧道的稳定性进行安全评估和如何确定临界状态下隧道围岩潜在破坏面,对从事隧道理论研究的学者和工程技术人员尤为重要。传统的研究方法主要是经典土力学方法和有限元法,但在解决上述问题时这两种方法均存在一定的局限性。极限分析上限定理,不但能够计算出接近实际情况的破坏荷载,而且可以获得相应的临界破坏面。因此,极限分析上限法是解决上述隧道工程稳定性问题的有效途径之一。本论文主要以极限分析上限定理为基础,结合数值方法和解析方法,对复杂条件下深埋和浅埋隧道的稳定性进行研究,主要研究内容如下：
(1)结合强度折减法和极限分析上限定理,通过对土体原始的抗剪强度指标进行折减,并利用内外能耗功率相等推导出浅埋隧道整体安全系数的目标函数。采用序列二次优化迭代方法对此目标函数进行优化,得到了浅埋隧道能量耗散最小意义下的安全系数,从而对浅埋隧道稳定性做出评价。
(2)根据浅埋隧道开挖面的主动和被动破坏模式,采用强度折减法和上限定理,构建了浅埋隧道开挖面安全系数的目标函数,并通过优化计算得到了隧道开挖面的最小安全系数。考虑实际工程中遇到的各种影响因素后,得到了各个因素作用下隧道开挖面安全系数的上限解,并就各个参数对安全系数的影响进行了详细的讨论。
(3)针对浅埋岩质隧道顶部围岩的破坏特征,构建了一种二维曲线型破坏机制。根据上限定理,利用Hoek-Brown破坏准则和变分法推导出了隧道顶部围岩塌落面的解析表达式。在此基础上,将孔隙水压力功率引入上限定理的虚功率方程中,研究了孔隙水压力作用下深埋隧道顶部围岩塌落面的形状。
(4)构建了深埋隧道顶部围岩的三维破坏机制,通过计算隧道顶部三维塌落体的内能耗散功率和外力功率获得了隧道围岩塌落面方程的目标函数。利用变分法求出了此目标函数能量耗散最优意义下的塌落面解析方程,根据此方程绘制了不同参数下深埋隧道顶部围岩三维塌落体的形状。
(5)将三维旋转体型破坏机制引入浅埋矩形隧道的上限分析中,采用变分法和数值软件绘制了浅埋矩形隧道顶部围岩塌落体的形状。考虑不同围岩参数、地表荷载和支护力对浅埋隧道顶部塌落体形状的影响,得到了隧道塌落体形状随各参数变化的规律。
(6)在前述研究的基础上,根据内外能耗计算和变分原理,推导出锚杆作用下深埋隧道顶部围岩塌落面形状的显示解。通过对参数分析,得到了深埋隧道围岩塌落面形状和塌落范围随锚杆支护参数变化的规律。
(7)基于南京地铁三号线星火路站～高新路站区间隧道工程,采用数值模拟方法和极限分析上限定理分别计算了隧道拱顶围岩塌落面的形状,将研究成果应用于实际工程。
The issue of tunnel stability is one of the essential problems in tunnel engineering. The assessment of tunnel stability when the supporting condition is known and the determination of potential failure surface for tunnel surrounding rock at critical state are especially important for scholars and engineers in their theoretical tunnel studies. There are limitations when the conventional soil mechanics and finite element method are employed to solve these problems. However, the application of the upper bound theorem of limit analysis in geotechnical stability analysis can not only derive the actual collapse load but also obtain the critical failure surface. Therefore, the upper bound theorem of limit analysis is one of the effective methods to solve the problems in tunnel engineering as mentioned above. Based on the upper bound theorem of limit analysis, using analytical and numerical methods, this dissertation studies the stability problems of deep and shallow tunnel for various complex factors. The main content of research is as follows:
(1) By combining the strength reduction method with the upper bound theorem, the objective function of factor of safety for shallow tunnel is derived from reducing the original soil strength parameters and virtual work equation. Using the sequential quadratic programming to optimize the objective function, the upper bound solution of factor of safety for shallow tunnel is obtained and the assessment of tunnel stability is conducted.
(2) Based on the collapse and blow-out failure mechanisms, the objective function of factor of safety for tunnel face is constructed by using the strength reduction method and the upper bound theorem. By introducing the influence factor of actual project into the upper bound analysis, the upper bound solution of factor of safety for tunnel face under each factor is obtained with the help of optimization calculation and the effect of parameters on the factor of safety is studied.
(3) To illustrate the collapsing feature of surrounding rock for shallow tunnel roof, a two-dimensional curved failure mechanism is constructed. Using the Hoek-Brown failure criterion and the variational approach, the analytical solution of collapsing surface for surrounding rock over shallow tunnel roof is derived in the framework of upper bound theorem. Furthermore, by introducing the power of pore pressure as a power of external force in the virtual work equation, the upper solution for the shape of collapsing surface over deep tunnel roof subjected to pore pressure is obtained.
(4) To achieve three-dimensional stability analysis for collapse block of a deep tunnel roof, a three-dimensional rotational failure mechanism is constructed. By calculating the rate of energy dissipation and the external rate of work in the failure mechanism, an objective function which includes the equation of collapsing surface is obtained. With the help of variational approach, the analytic expression of surface equation for the three-dimensional collapsing block is derived, and the shapes of three-dimensional collapsing surface for deep tunnel under different rock parameters are drawn.
(5) By extending the three-dimensional stability analysis method for deep tunnel to shallow tunnel, the shapes of three-dimensional collapsing surface of shallow tunnel are derived. Considering the influence of different rock parameters, surcharge load, and supporting pressure on the shape of collapsing surface, the change law of each parameter for the shape of collapsing surface is obtained.
(6) On the basis of the research results mentioned above, the analytical solution of collapsing surface for deep tunnel with the effect of rockbolt are derived from energy dissipation calculation and variational approach. By analyzing the size of collapsing block for deep tunnel under different rockbolt parameters, the change laws of each parameter for rockbolt are obtained.
(7) Based on the observed geological data of running tunnel in Nanjing Metro, using numerical simulation and the analytical method mentioned above, the shape of collapsing surface for surrounding rock over tunnel roof is calculated, and the research results are thus applied to practical projects.
(1)结合强度折减法和极限分析上限定理,通过对土体原始的抗剪强度指标进行折减,并利用内外能耗功率相等推导出浅埋隧道整体安全系数的目标函数。采用序列二次优化迭代方法对此目标函数进行优化,得到了浅埋隧道能量耗散最小意义下的安全系数,从而对浅埋隧道稳定性做出评价。
(2)根据浅埋隧道开挖面的主动和被动破坏模式,采用强度折减法和上限定理,构建了浅埋隧道开挖面安全系数的目标函数,并通过优化计算得到了隧道开挖面的最小安全系数。考虑实际工程中遇到的各种影响因素后,得到了各个因素作用下隧道开挖面安全系数的上限解,并就各个参数对安全系数的影响进行了详细的讨论。
(3)针对浅埋岩质隧道顶部围岩的破坏特征,构建了一种二维曲线型破坏机制。根据上限定理,利用Hoek-Brown破坏准则和变分法推导出了隧道顶部围岩塌落面的解析表达式。在此基础上,将孔隙水压力功率引入上限定理的虚功率方程中,研究了孔隙水压力作用下深埋隧道顶部围岩塌落面的形状。
(4)构建了深埋隧道顶部围岩的三维破坏机制,通过计算隧道顶部三维塌落体的内能耗散功率和外力功率获得了隧道围岩塌落面方程的目标函数。利用变分法求出了此目标函数能量耗散最优意义下的塌落面解析方程,根据此方程绘制了不同参数下深埋隧道顶部围岩三维塌落体的形状。
(5)将三维旋转体型破坏机制引入浅埋矩形隧道的上限分析中,采用变分法和数值软件绘制了浅埋矩形隧道顶部围岩塌落体的形状。考虑不同围岩参数、地表荷载和支护力对浅埋隧道顶部塌落体形状的影响,得到了隧道塌落体形状随各参数变化的规律。
(6)在前述研究的基础上,根据内外能耗计算和变分原理,推导出锚杆作用下深埋隧道顶部围岩塌落面形状的显示解。通过对参数分析,得到了深埋隧道围岩塌落面形状和塌落范围随锚杆支护参数变化的规律。
(7)基于南京地铁三号线星火路站～高新路站区间隧道工程,采用数值模拟方法和极限分析上限定理分别计算了隧道拱顶围岩塌落面的形状,将研究成果应用于实际工程。
The issue of tunnel stability is one of the essential problems in tunnel engineering. The assessment of tunnel stability when the supporting condition is known and the determination of potential failure surface for tunnel surrounding rock at critical state are especially important for scholars and engineers in their theoretical tunnel studies. There are limitations when the conventional soil mechanics and finite element method are employed to solve these problems. However, the application of the upper bound theorem of limit analysis in geotechnical stability analysis can not only derive the actual collapse load but also obtain the critical failure surface. Therefore, the upper bound theorem of limit analysis is one of the effective methods to solve the problems in tunnel engineering as mentioned above. Based on the upper bound theorem of limit analysis, using analytical and numerical methods, this dissertation studies the stability problems of deep and shallow tunnel for various complex factors. The main content of research is as follows:
(1) By combining the strength reduction method with the upper bound theorem, the objective function of factor of safety for shallow tunnel is derived from reducing the original soil strength parameters and virtual work equation. Using the sequential quadratic programming to optimize the objective function, the upper bound solution of factor of safety for shallow tunnel is obtained and the assessment of tunnel stability is conducted.
(2) Based on the collapse and blow-out failure mechanisms, the objective function of factor of safety for tunnel face is constructed by using the strength reduction method and the upper bound theorem. By introducing the influence factor of actual project into the upper bound analysis, the upper bound solution of factor of safety for tunnel face under each factor is obtained with the help of optimization calculation and the effect of parameters on the factor of safety is studied.
(3) To illustrate the collapsing feature of surrounding rock for shallow tunnel roof, a two-dimensional curved failure mechanism is constructed. Using the Hoek-Brown failure criterion and the variational approach, the analytical solution of collapsing surface for surrounding rock over shallow tunnel roof is derived in the framework of upper bound theorem. Furthermore, by introducing the power of pore pressure as a power of external force in the virtual work equation, the upper solution for the shape of collapsing surface over deep tunnel roof subjected to pore pressure is obtained.
(4) To achieve three-dimensional stability analysis for collapse block of a deep tunnel roof, a three-dimensional rotational failure mechanism is constructed. By calculating the rate of energy dissipation and the external rate of work in the failure mechanism, an objective function which includes the equation of collapsing surface is obtained. With the help of variational approach, the analytic expression of surface equation for the three-dimensional collapsing block is derived, and the shapes of three-dimensional collapsing surface for deep tunnel under different rock parameters are drawn.
(5) By extending the three-dimensional stability analysis method for deep tunnel to shallow tunnel, the shapes of three-dimensional collapsing surface of shallow tunnel are derived. Considering the influence of different rock parameters, surcharge load, and supporting pressure on the shape of collapsing surface, the change law of each parameter for the shape of collapsing surface is obtained.
(6) On the basis of the research results mentioned above, the analytical solution of collapsing surface for deep tunnel with the effect of rockbolt are derived from energy dissipation calculation and variational approach. By analyzing the size of collapsing block for deep tunnel under different rockbolt parameters, the change laws of each parameter for rockbolt are obtained.
(7) Based on the observed geological data of running tunnel in Nanjing Metro, using numerical simulation and the analytical method mentioned above, the shape of collapsing surface for surrounding rock over tunnel roof is calculated, and the research results are thus applied to practical projects.
引文
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