拓扑优化方法在面板堆石坝分区设计中的应用

面板堆石坝因其经济、可靠、广泛适应性和环保等显著优点受到坝工界的欢迎,但面板坝尤其是高面板坝普遍存在面板断裂问题。故因面板断裂而造成的面板坝事故实例很多。面板断裂的主要原因之一是坝体内坝料分布不合理使得坝体与面板在自重与水压力作用下变形差异较大,因此,坝料在坝体内部的布局亦即坝料分区设计极为重要。该文以天生桥一级混凝土面板堆石坝为例,以坝体刚度最大为目标,根据坝料切线模量的差异,将坝料分为多种材料,建立材料集合,采用连续体拓扑优化方法优化出高面板坝坝料的布局方案,从而克服以往完全依赖经验给出的分区设计缺陷。另外,在优化分析中,以单元的材料号作为设计变量,同时基于准则法给出了设计变量的更新方案,即应变能密度大的单元须具有高模量材料。规避了传统梯度法或遗传算法无法解决离散设计变量数目庞大的困难。为确保算法稳定,本方法迭代过程中每次仅更新不超过5%的总单元数的材料号。结果表明,优化后的材料布局与传统分区存在明显差异:高模量材料分布在上游下侧、各种材料分布随模量依次自上游向下游变化、材料边界坡比均不低于1:0.8。与原设计相比,优化后的面板在水压力作用下变形小,分布均匀,有利于阻止面板发生断裂。从而证明该方法可为此类工程实践提供具有理论基础的参考设计。

Topology optimization method for zoning of high concrete face rockfill dam

Abstract: Concrete face rockfill dam (CFRD) is very popular in modern dam engineering applications due to its low cost, stability, adaptability and environment friendly. In CFRD engineering, many accidents are caused by the cracks of face plates. Especially, most of high CFRDs (over 100 m) have cracks in their face plates that reduce the safety of dams in operation. One of the main reasons for the cracks in face plates of a high CFRD is difference between the deformation of the face plates and dam body under gravity and upstream water pressure. Clearly, the deformation of dam body is determined by not only gravity and the water pressure, but also the distribution of filled materials. Therefore, the layout of the materials in dam body is essential to CFRD engineering. Taking TSQ-1 CFRD as an example, the best partition form of dam material within cross-section of a high CFRD was analyzed by continuum topology optimization. In traditional design, the zoning of material was given mostly according to designer's experiences and however, the intuitive method is not feasible because the height of CFRD is over 200 m. In this research, a continuum topology optimization method was proposed to find the optimal partition of the filled materials in CFRD. Considering the differences among the elasticity of materials in dam body, a material set was formed with the materials in respect to their tangential moduli. The deformation of structure was solved using finite element (FE) method and the material number of each FE was chosen within the material set. The purpose of the present research was to find the optimal material numbers in finite elements in design domain. A heuristic method was presented and similar to evolutionary structural optimization (ESO) as considering the update rule of material properties in optimization process. Here, a criterion was adopted to renew the design variables, i.e., the material numbers with respect to the tangential modulus of materials in dam body. To keep the stability of algorithm, no more than 5% of total elements' material number will be renewed in iteration. The results indicated that there were obvious differences between the layout of optimized material and that of the traditional partition. High modulus materials were located in the lower side of the upper reaches and various materials changed gradually with respect to the moduli from the upstream to downstream. And boundary slope ratios of materials were not lower than 1:0.8. Compared with the original design, deformation of panel in optimized dam was slighter and more uniform under water pressure, which helps to prevent face plate from breaking.