三维有限元分析隧道开挖收敛损失与纵剖面变形曲线关系研究

采用实验室研发的三维有限元程序,运用隧道收敛–约束法的分析模式,针对岩体弹性参数、初始应力与隧道径向位移等影响因素,探讨有支撑与无支撑情况下的隧道开挖收敛损失与纵剖面变形曲线关系。采用纵剖面变形曲线的研究结果,并与三维有限元数值计算结果相比较,探讨收敛损失的影响。由隧道收敛–约束法理论分析结果与三维有限元数值计算结果可知:(1)确立隧道开挖收敛损失与纵剖面变形曲线的关系;(2)隧道纵剖面变形曲线的归一化处理方式,可消除岩体参数、初始应力和隧道收敛的位置等因素影响;(3)在弹性条件下,隧道开挖面产生的前期位移量约为最终位移量的25%～36%;(4)由二维纵剖面变形曲线的分布,可计算并获得隧道开挖收敛损失值、了解隧道开挖工作面效应的三维影响,进而能计算分析岩体结构的应力与位移等变化量。

隧道开挖地层反应曲线的外显分析

收敛–约束法理论是应用于隧道支撑设计的简化分析方法,所使用的约束损失是该分析方法的关键因子。基于隧道开挖前进效应与约束损失的关系,建立隧道掘进效应函数,并采用约束损失的递增方法与简易试算表工具,同时依据应力–位移力学理论模式,推导在静水应力条件下圆形隧道开挖于弹塑性地层的解析解,进而提出模拟地层反应曲线弹塑性非线性行为的外显分析法。其分析结果包含约束损失递增方法的计算内容与步骤说明,以及约束损失弹性极限值、塑性半径、弹塑性区的径向应力与径向位移。此分析法与研发的有限元分析结果比较显示,二者呈现相似且一致的非线性趋势。

GLOBAL CONVERGENCE OF A CLASS OF OPTIMALLY CONDITIONED SSVM METHODS

This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are globally convergent for general convex functions.

Initial support distance of a non-circular tunnel based on convergence constraint method and integral failure criteria of rock

For deep tunnel projects,selecting an appropriate initial support distance is critical to improving the self-supporting capacity of surrounding rock.In this work,an intuitive method for determining the tunnel’s initial support distance was proposed.First,based on the convergence-confinement method,a three-dimensional analytical model was constructed by combining an analytical solution of a non-circular tunnel with the Tecplot software.Then,according to the integral failure criteria of rock,the failure tendency coefficients of hard surrounding rock were computed and the spatial distribution plots of that were constructed.On this basis,the tunnel’s key failure positions were identified,and the relationship between the failure tendency coefficient at key failure positions and their distances from the working face was established.Finally,the distance from the working face that corresponds to the critical failure tendency coefficient was taken as the optimal support distance.A practical project was used as an example,and a reasonable initial support distance was successfully determined by applying the developed method.Moreover,it is found that the stability of hard surrounding rock decreases rapidly within the range of 1.0D(D is the tunnel diameter)from the working face,and tends to be stable outside the range of 1.0D.

Prediction of plastic zone size around circular tunnels in non-hydrostatic stress field

This paper discusses the calculation of plastic zone properties around circular tunnels to rock-masses that satisfy the Hoek–Brown failure criterion in non-hydrostatic condition,and reviews the calculation of plastic zone and displacement,and the basis of the convergence–confinement method in hydrostatic condition.A two-dimensional numerical simulation model was developed to gain understanding of the plastic zone shape.Plastic zone radius in any angles around the tunnel is analyzed and measured,using different values of overburden(four states)and stress ratio(nine states).Plastic zone radius equations were obtained from fitting curve to data which are dependent on the values of stress ratio,angle and plastic zone radius in hydrostatic condition.Finally validation of this equation indicate that results predict the real plastic zone radius appropriately.

ON THE CONVERGENCE OF A NEW HYBRID PROJECTION ALGORITHM

For unconstrained optimization, a new hybrid projection algorithm is presented m the paper. This algorithm has some attractive convergence properties. Convergence theory can be obtained under the condition that Δ↓f（x） is uniformly continuous. If Δ↓f（x） is continuously differentiable pseudo-convex, the whole sequence of iterates converges to a solution of the problem without any other assumptions. Furthermore, under appropriate conditions one shows that the sequence of iterates has a cluster-point if and only if Ω＊ ≠ θ. Numerical examples are given at the end of this paper.

An M-Objective Penalty Function Algorithm Under Big Penalty Parameters

Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software,which makes them impossible to find out an optimal solution to constrained optimization problems.In this paper,a novel penalty function(called M-objective penalty function) with one penalty parameter added to both objective and constrained functions of inequality constrained optimization problems is proposed.Based on the M-objective penalty function,an algorithm is developed to solve an optimal solution to the inequality constrained optimization problems,with its convergence proved under some conditions.Furthermore,numerical results show that the proposed algorithm has a much better convergence than the classical penalty function algorithms under big penalty parameters,and is efficient in choosing a penalty parameter in a large range in Matlab software.

Derivation and Global Convergence for Memoryless Non-quasi-Newton Method

In this paper, a new class of memoryless non-quasi-Newton method for solving unconstrained optimization problems is proposed, and the global convergence of this method with inexact line search is proved. Furthermore, we propose a hybrid method that mixes both the memoryless non-quasi-Newton method and the memoryless Perry-Shanno quasi-Newton method. The global convergence of this hybrid memoryless method is proved under mild assumptions. The initial results show that these new methods are efficient for the given test problems. Especially the memoryless non-quasi-Newton method requires little storage and computation, so it is able to efficiently solve large scale optimization problems.