摘要
隧道稳定可靠度评价一直是隧道工程领域所面临的重大问题之一。在此评价过程中,作为可靠度理论不可或缺的组成部分,以及实施可靠性优化设计与风险预测的必要环节,隧道稳定可靠度计算分析方法研究具有至关重要的地位,其计算结果合理性与准确性不仅直接关系到隧道工程安全可靠程度,而且也将对其相应工程决策产生重大影响。为此,本文将在考虑隧道自身具备的有关工程特性基础上,针对其可靠度计算过程中功能函数的构建与不确定因素的描述方式这两个关键性问题,分别从概率与非概率角度对隧道稳定可靠度计算分析方法与理论开展研究,进而在隧道工程中进行应用。
首先,基于概率可靠度方法,在构建功能函数过程中,针对目前隧道隐式功能函数可靠度计算存在的问题,以常见的锚喷支护为例,依据围岩与支护结构之间相互作用机理,通过采用围岩剪切滑移理论、薄壁圆筒公式以及锚杆与围岩共同变形理论建立了相应的结构功能函数,并在一次二阶矩理论框架内,引入了差分方法替代功能函数偏导运算。在此基础上,通过Taylor级数展开将上述功能函数转化为以可靠指标为未知变量的形式,同时结合复合函数求导法则推导出可靠指标迭代逼近求解公式,进而建立了一种适用于隧道工程隐式功能函数可靠度求解的简便实用方法。
其次,鉴于隧道工程领域隐式功能函数的复杂性特征,在上章分析方法基础上,对其仍存在的问题通过引入响应面函数建模思路开展相应研究。基于围岩变形判别准则的功能函数,分析了经典二次响应面法试验点选取方式,由统计矩与随机参数分布概型之间关系,并根据随机参数不同分布形式的隧道实际工程特性,指出经典二次响应面法取样方式存在无法反映各参数分布曲线实际特征,而仅适用于其为对称形态的缺陷。由此引入Rosenblueth方法来考虑偏度系数对随机参数分布特征影响,进而采用偏度纠正系数对之实施偏度矫正,据此形成的响应面法能适用于隧道实际工程中随机参数分布形式的多样性特征。工程算例结果表明该方法能使计算结果精度得到较大改善和提高。
再次,针对以序列响应面技术为主要代表的经典二次响应面法继续进行深入探讨。通过进一步结合隧道工程中参数耦合作用关系(即因素间相互作用),以及各参数对隧道稳定性能不同重要影响程度的实际工程特性,从序列响应面法自身前提条件存在问题入手,提出采用包含交叉项的完全二次函数形式以考虑参数耦合作用,同时,引入回归正交组合试验设计手段,并结合显著性检验原理,探讨了各参数对隧道稳定性能影响程度的判别方法,形成了具有识别参数重要程度的响应面模型优化技术。然后,根据各参数之实际变化范围由可靠指标几何意义求解可靠指标,建立了更具工程合理性的隧道隐式功能函数二次响应面可靠度计算方法。工程实例分析验证了该方法的有效性与合理性。
为进一步在隧道工程领域探讨利用响应面函数建模手段处理隐式功能函数可靠度问题时的适用性,依据其自身稳定性力学状态高度复杂的基本工程特性,综合考虑了函数表达关系与取样方式。在响应面函数具体表达关系上,针对二次多项式及现有其它函数形式局限性,引入了理论上更趋严谨、对复杂非线性问题处理更有效的支持向量机回归方法；对于试验样本点选取方式,采用对复杂非线性模型估计适应能力更强、计算效率更高的均匀设计试验方法。上述两者结合形成了一种更趋完善的隧道可靠度响应面技术,拓宽了其解决隧道复杂隐式功能函数可靠度问题的工程适用范围。通过举例分析与验证展示了该方法的正确性与工程参考价值。
最后,在以上概率方法基础上,为更进一步丰富和完善隧道稳定可靠度计算分析方法,针对该领域不确定性数据匮乏、不易获得不确定性因素足够信息而导致概率方法求解之先决条件无法满足的实际状况,基于不确定因素集合描述方式,从非概率评判角度对隧道可靠度分析方法开展研究。通过引进鲁棒可靠性思想,采用Information-Gap(Info-Gap)鲁棒性理论将隧道响应输出模型中不确定参量以Info-Gap集合模型来描述,并基于稳定性力学模式,由输出模型响应值与临界值之间关系构建鲁棒函数,据此将隧道发生失效前可容许不确定参量之最大波动幅度值定义为鲁棒可靠指标,进而建立了新的基于Info-Gap鲁棒性分析模型的隧道非概率可靠度评价体系。通过实例分析与讨论,表明了该模型具有较强的可行性及一定的工程应用前景。
The reliability evaluation of tunnel stability is invariably one of the significant issues encountered in the domain of tunnel engineering. Throughout the whole evaluation process, as an indispensable element of the reliability theory, as well as an essential procedure in performing reliability optimization designs and risk predictions, the investigation on the analysis method of reliability calculations plays a paramount role for the stability of tunnels, in which the rationality and precision of the calculated results are not only directly related to the level of safety and reliability of tunnels, but also have marked influences on the corresponding decision-making in such a field. For that reason, based on the consideration of associated engineering properties residing in the tunnel itself, the explorations of analysis method and theory of reliability calculations for tunnel stability are implemented from the probabilistic and non-probabilistic viewpoint, respectively, aiming at the two critical problems involved in the reliability analysis (i.e., the development of performance functions and the description of uncertainty factors). These outcomes could then have possible applications in tunnel engineering.
Firstly, in the context of probabilistic methods, when developing the performance function, a difference approximation-based technique used to calculate the derivatives is proposed according to the limitations in reliability calculations for implicit performance functions. Taking the conventional primary support installed by rockbolts and shotcrete lining as an example, a corresponding performance function is built via the shear failure theory, the thin-walled cylinder formula and the consistent deformation theory of the ground-support interaction analysis. Within a framework of the first-order reliability method, a difference approximation is thereby introduced to estimate the partial derivatives of the implicit performance function. On this basis, such a performance function can be transformed into an expression involving a single unknown described as the reliability index with the aid of Taylor's formula, and then the resulting approximate iterative procedure for determining the reliability index can be rendered by incorporating the derivation rule of compound function. A straightforward and practical algorithm for the non-explicit performance functions in tunnel engineering is hence presented.
Subsequently, in view of the complexity of the implicit performance function in tunnelling, the exploration is carried out in order to circumvent the difficulties still encountered in reliability analysis by introducing the function modelling of the response surface. In conformity with the performance function provided by the deformation principle of the surrounding rock, the sampling strategy of the classical response surface method (RSM) is analyzed. By consideration of the relationships between the statistical moments and the probability distributions of stochastic variables, and according to those various distributions exhibited actually in tunnel engineering, one key limitation of the classical RSM is that the sampling strategy can be incapable of reflecting the actual characteristics of distribution curves, but be only applicable to those curves behaved symmetrically. It is therefore recommended to use the Rosenblueth method to account for the effects of skewness coefficient on the configuration of distribution curves, whose skewness is rectified through certain coefficients. The resulting RSM that has the applicability in practical situations for various distributions of random variables is then presented, the example analysis shows that such a method can, to a certain extent, ameliorate and enhance the accuracy of computational results.
Thirdly, much effort continues to direct towards the investigation on the sequential response surface technique, as the major representative of the classical RSM, by combining the engineering properties related to the coupling actions between variables (or interactions between factors) and different levels of the importance among those variables. According to the difficulties arising in the prerequisites for the sequential response surface method, a complete quadratic polynomial including the cross terms is employed to consider the coupling action between those variables. By integrating the regression analysis of orthogonal composite design with the statistical significance testing, a discriminant tool serving to the delineation of the effect of various factors on tunnel stability is provided, and a resulting optimum approach is then proposed for the response surface model to identify the importance level of basic variables. On this basis, the reliability index can be obtained through its geometrical meaning when knowing the actual interval of various variables. Consequently, a more reasonable quadratic RSM for reliability computations of tunnels is established, whose effectiveness and reasonableness are then validated using the illustrative example.
For the purpose of performing further discussion on the applicability of the response surface modelling treated for the reliability problem, two fundamental issues posed in the RSM, viz., the function expression and the sampling strategy, are both taken into account according to the highly complicated mechanical state in tunnelling. For the expression of the response surface, the support vector regression approach is offered, which is much stricter in theory and more effective for complex nonlinear problems than the quadratic polynomial and some other existing functions. As regards the sampling strategy associated to the experimental design, the uniform design method is introduced, which is more applicable to the nonlinear model estimation and more efficient in computations than other design approaches. Such a combination of the two above devices tends to perfect the response surface technique, thus widening its applicability in solving the tunnel reliability problems of complicated performance functions. The correctness and referential value of the suggested method are demonstrated by the example analysis and verification.
Eventually, on the basis of the probabilistic treatments in the above chapters, a special attention is devoted to enriching and improving the analysis method of reliability calculations for tunnel stability. Owing to the fact that the data on the uncertainties are quite limited and the uncertainty information is rather unavailable in tunnel engineering, the essential prerequisite in the probabilistic concept is not fulfilled. In this environment, the investigation on the reliability method is performed based on the set model of uncertainties from the non-probabilistic perspective. By introducing the concept of robust reliability, the Information-Gap (Info-Gap) robust theory is provided to handle the uncertain variables quantitatively with the Info-Gap set model. According to the mechanical mode in tunnelling, the robustness function is formulated by correlating the response value with the critical value of the output model. It is then followed by the definition of the robust reliability index, indicating that the tunnel performance could suffer the greatest horizon of the fluctuation of uncertain variables before failure. Therefore, a novel non-probabilistic evaluation methodology is developed based on the Info-Gap robustness model. The example analyses and discussions are presented to demostrate the proposed model with relatively favorable feasibility and a certain perspective of practical applications.
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