隧道围岩特性曲线数值模拟与分析

由于围岩特性曲线中只有圆形坑道才有解析解,对马蹄形坑道只能近似地将其转换成圆形[1],加上其它因素,如围岩原始数据、原始应力场、初始位移等的确定问题,使得特征曲线法在一般衬砌设计,特别是衬砌标准图设计中难以应用。笔者采用弹塑性有限元方法绘制了不同埋深、各种围岩级别下的铁路标准设计单、双线毛洞的围岩特征曲线,得出不同围岩级别、不同埋深、不同洞形和尺寸下围岩特性曲线的变化规律。对特性曲线法在隧道衬砌设计中的应用有实际意义。

大断面隧道软弱围岩-支护系统稳定性分析

采用室内试验研究手段获得隧道围岩力学特性,以Mohr-Coulomb弹塑性模型及应变软化模型为基础,采用FLAC3D数值模拟软件,构建三维数值模型,计算深埋隧道围岩特征曲线及纵剖面变形曲线,并对隧道围岩及支护结构安全性进行评价。结果表明:采用弹塑性模型计算所得的隧道围岩安全系数低于应变软化模型所得的安全系数,表明采用弹塑性模型进行支护结构设计时,支护结构安全性较低,设计中可能会增加支护材料费用,而考虑应变软化条件下的围岩安全系数更加接近于工程实际;采用极限应变值或支护结构极限承载压力所获得的围岩—支护系统安全系数较为接近,说明两种方法的差异较小,均可用于隧道围岩支护结构优化设计,采用收敛—约束法计算隧道安全稳定性更加直观,对工程实际具有一定指导作用。

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.