高拱坝地震损伤开裂的大型数值模拟
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摘要
围绕西部大开发的战略决策,实施西电东送,多座高坝大库在西南地区进行建设。其中拱坝坝型得到广泛采用。鉴于西部强震区拱坝抗震安全的重要性,本文依托国家自然科学基金重点项目(50139010)和(90510018),针对强震区高拱坝抗震安全的大规模数值模拟进行了深入的研究。
1.高拱坝在强震作用下可能出现损伤、产生裂缝,对高拱坝进行全面的抗震安全评价应考虑这种非线性行为。混凝土在细观尺度上是非均匀的,细观非均匀性已成为研究混凝土结构损伤开裂的一个突破口。对高拱坝来说,无法也无必要精确界定这种非均匀性。在将拱坝有限元网格足够细分的前提下,近似认为单元内部为均匀材料,细观不均匀性的影响通过单元的材料属性随机分布来表征。同时,单元尺寸足够小时,塑性和各向异性等被弱化,采用弹性损伤本构关系和带拉伸截断的摩尔-库仑准则来模拟混凝土的非线性行为。对大岗山拱坝的地震损伤破坏模拟获得了和振动台模型试验吻合的结果,证明了该数值模型的有效性。同时,这种模型实施方便、计算效率高,便于大规模计算,而且可模拟拱坝从出现微裂缝到出现宏观裂缝的过程。在此基础上,研究了拱坝横缝以及无限地基辐射阻尼对拱坝损伤破坏的影响。
2.目前可用于三维高拱坝大规模高效数值模拟的拱坝-地基相互作用方法少见。Wolf和Song提出的阻尼溶剂抽取法通过在近场地基有限域内施加人工阻尼再移频抽取的方法,模拟无限地基辐射效应。该方法避免了卷积,具有应用于大规模计算的潜力。然而,目前该方法在相互作用中的应用仅限于二维问题,且计算效率低、计算容量小。本文将该方法推广至三维,并在算法和矩阵存储格式方面进行了专门研究,建立了针对大规模计算的高拱坝-无限地基动力相互作用时域模型。对该模型进行了算例验证并建议了参数取值:dl/b=1～1.5及l=2～3b。其中b为基础特征尺寸,l为地基模拟范围,d为施加的无量纲人工阻尼。该模型在高拱坝地震损伤破坏模拟中的应用表明,考虑无限地基辐射阻尼后,拱坝损伤破坏情况明显减轻。
3.有限元大规模分析中,若计算能力有限,可根据计算要求在有限元模型内布置疏密不等的网格,并采用特定的网格过渡技术来保证交界面处的协调性。本文提出了三种疏密网格过渡的方法。弹簧节理单元为在界面过渡单元的基础上,引入虚拟节点和子单元,在子单元中应用节理单元思想,并将虚拟节点凝聚掉,可保证界面两侧的位移和应变协调。主从自由度法是通过将界面非协调节点的位移表示成协调节点位移的函数,从而将非协调节点凝聚掉,可保证界面两侧的位移协调和刚度匹配。新型十三节点单元通过将母单元积分域分成四个子域,构造线性插值函数,然后分别在四个子域中进行数值积分,完全消除了普通变节点单元界面位移不协调的缺陷。三种模型的精度及实用性均经过验证,其中新型十三节点单元还应用于考虑无限地基辐射阻尼的高拱坝地震损伤破坏分析。
4.大型工程项目如高拱坝的快速精细大规模数值模拟对计算能力和速度提出了越来越高的要求,另一方面物理光速的限制以及Von Neuman体系本身的瓶颈使得串行计算机的发展不能满足需求。采用高性能并行计算是解决这一矛盾的根本途径。本文采用4台普通微机和高速网络,搭建了PC集群作为并行计算平台。并针对高拱坝的地震损伤破坏模拟,在Linux系统下研制开发了基于区域分解法和消息传递MPI库的并行计算程序PDPAD。该程序在测试中表现出了良好的可扩展性和加速比,具有高效求解大规模问题的能力。目前在4节点PC集群上已达到百万自由度的计算能力,而且在实际高拱坝的地震损伤破坏数值模拟中表现良好。
As an important part of the Western Development Strategy, West-East Power Transmission program promoted the construction of quite a few high dams, in which concrete arch dams have been widely employed. As we all know, the aseismic safety is crucial to high arch dams in southwest China. With the support from National Nature Science Foundation of China under Grants 50139010 and 90510018, in-depth research was conducted regarding the large-scale numerical simulation of high arch dams in strong earthquakes.
1. High arch dams may get fractured or damaged in strong earthquakes, which should be considered in its aseismic safety evaluation. As is known that concrete is inhomogeneous on the mesoscopic level, and taking advantage of this fact could better simulate the fracture process of concrete structures. However, as far as high concrete dams are concerned, it would be impossible and unnecessary to precisely simulate this inhomogeneity. If the arch dam is modeled with meshes fine enough, every mesh can be regarded as homogeneous, while the mesoscopic inhomogeneity is taken into account via random distribution of material properties of the element. In the meantime, the plasticity and anisotropism of every single element can be neglected. In the presented model for damage analysis of arch dams, elastic damage constitutive equations together with simple failure criterions, i.e., Mohr-Coulomb Principle with tension cut-off, are employed to simulate the nonlinearity of concrete. Taking the Dagangshan Arch Dam as an example, numerical result accords with results of shaking table test, which verifies the validity of the presented model. An important feature of this model is simplicity, which avails its application to large-scale computation. Last but not least important, the conversion from continuity to discontinuity can be simulated with this single model. On this basis, certain factors that affect the damage status of arch dams such as joints and radiation damping of the unbounded media are further investigated.
2. Much research work has been conducted in the field of structure-foundation interaction, but these work seldom focused on the large scale analysis of massive structures such as high arch dams. The Damping Solvent Extraction Method (DSEM) as proposed by Wolf and Song simulate radiation damping in a novel way. Artificial damping is introduced into the near field adjacent to the structure, and is extracted afterwards. Then the stiffness matrix of the unbounded media can be obtained by applying an assumption. DSEM avoided the convolution integral generally obssessing other methods and possesses the potential for application to large scale computation. However, DSEM is now only employed in 2D SSI problems, and pitifully with low computation efficiency and small capacity. By extending this model into 3D problems, together with in-depth research on the algorithm and matrix storage styles, a DSEM-based interaction model in the time domain for large scale computation of high arch dams is presented. Based on parametric study, relevant parameters are suggested:dl/b=1～1.5 and l=2～3b . Here d refers to the undimensional artificial damping, 1 is the size of the near field while b is the characteristic length of the foundation. The presented model is employed in the damage simulation of Dagangshan Arch Dam subjected to strong earthquakes. And it's observed that the damage of arch dam is greatly alleviated with the radiation damping considered.
3. With limited computational capacity for large scale finite element analysis, meshes of different sizes may be employed according to the significance of different parts of the system considered. Then techniques for transition between coarse and fine elements should be introduced. Three methods for transition are proposed, viz. the Springed Joint Method, the Master DOF (Degree of Freedom) Method and the 13-node element. The former is based on Qiang Tianchi's interface coupled method which was founded according to the least potential energy method. As in the Joint Element Method, with fictitious nodes and sub elements technique employed, the integral in Qiang Tianchi's version is simplified and transition between two sets of coordination which requires high precision is avoided. The Master DOF Method utilizes displacement constraint and needs only simple matrix operation in application. While in the 13-node element, the integration region is divided into four sub-regions, each with linear interpolating functions. All the three methods guarantee the displacement coordination between coarse elements and fine elements. Their accuracy and feasibility were verified, and the 13-node element has been employed in the damage simulation of high arch dams subjected to strong earthquakes.
4. The aseismic evaluation of high arch dams calls for large-scale and efficient numerical simulation. Personal computer, despite its rapid development, can hardly meet the needs. High performance parallel computing is the ultimate solution to this problem. A PC cluster was setup with 4 personal computers and high-speed network to be the parallel computation platform. And a parallel program PDPAD was developed for numerical simulation of damage process of high arch dams in strong earthquakes. Based on Domain Decomposition Method, the proposed damage simulation model as detailed in Chapter 2 is programmed to parallel finite element codes with MPI (Message Passing Interface) in FORTRAN 9.0 on Linux Redhat 9.0. PDPAD exhibits high scalability and speedup ratio and has the ability for large scale computation. It is employed in the damage process simulation of Dagangshan Arch Dam and can handle more than one million DOFs on the 4-node platform.
1.高拱坝在强震作用下可能出现损伤、产生裂缝,对高拱坝进行全面的抗震安全评价应考虑这种非线性行为。混凝土在细观尺度上是非均匀的,细观非均匀性已成为研究混凝土结构损伤开裂的一个突破口。对高拱坝来说,无法也无必要精确界定这种非均匀性。在将拱坝有限元网格足够细分的前提下,近似认为单元内部为均匀材料,细观不均匀性的影响通过单元的材料属性随机分布来表征。同时,单元尺寸足够小时,塑性和各向异性等被弱化,采用弹性损伤本构关系和带拉伸截断的摩尔-库仑准则来模拟混凝土的非线性行为。对大岗山拱坝的地震损伤破坏模拟获得了和振动台模型试验吻合的结果,证明了该数值模型的有效性。同时,这种模型实施方便、计算效率高,便于大规模计算,而且可模拟拱坝从出现微裂缝到出现宏观裂缝的过程。在此基础上,研究了拱坝横缝以及无限地基辐射阻尼对拱坝损伤破坏的影响。
2.目前可用于三维高拱坝大规模高效数值模拟的拱坝-地基相互作用方法少见。Wolf和Song提出的阻尼溶剂抽取法通过在近场地基有限域内施加人工阻尼再移频抽取的方法,模拟无限地基辐射效应。该方法避免了卷积,具有应用于大规模计算的潜力。然而,目前该方法在相互作用中的应用仅限于二维问题,且计算效率低、计算容量小。本文将该方法推广至三维,并在算法和矩阵存储格式方面进行了专门研究,建立了针对大规模计算的高拱坝-无限地基动力相互作用时域模型。对该模型进行了算例验证并建议了参数取值:dl/b=1～1.5及l=2～3b。其中b为基础特征尺寸,l为地基模拟范围,d为施加的无量纲人工阻尼。该模型在高拱坝地震损伤破坏模拟中的应用表明,考虑无限地基辐射阻尼后,拱坝损伤破坏情况明显减轻。
3.有限元大规模分析中,若计算能力有限,可根据计算要求在有限元模型内布置疏密不等的网格,并采用特定的网格过渡技术来保证交界面处的协调性。本文提出了三种疏密网格过渡的方法。弹簧节理单元为在界面过渡单元的基础上,引入虚拟节点和子单元,在子单元中应用节理单元思想,并将虚拟节点凝聚掉,可保证界面两侧的位移和应变协调。主从自由度法是通过将界面非协调节点的位移表示成协调节点位移的函数,从而将非协调节点凝聚掉,可保证界面两侧的位移协调和刚度匹配。新型十三节点单元通过将母单元积分域分成四个子域,构造线性插值函数,然后分别在四个子域中进行数值积分,完全消除了普通变节点单元界面位移不协调的缺陷。三种模型的精度及实用性均经过验证,其中新型十三节点单元还应用于考虑无限地基辐射阻尼的高拱坝地震损伤破坏分析。
4.大型工程项目如高拱坝的快速精细大规模数值模拟对计算能力和速度提出了越来越高的要求,另一方面物理光速的限制以及Von Neuman体系本身的瓶颈使得串行计算机的发展不能满足需求。采用高性能并行计算是解决这一矛盾的根本途径。本文采用4台普通微机和高速网络,搭建了PC集群作为并行计算平台。并针对高拱坝的地震损伤破坏模拟,在Linux系统下研制开发了基于区域分解法和消息传递MPI库的并行计算程序PDPAD。该程序在测试中表现出了良好的可扩展性和加速比,具有高效求解大规模问题的能力。目前在4节点PC集群上已达到百万自由度的计算能力,而且在实际高拱坝的地震损伤破坏数值模拟中表现良好。
As an important part of the Western Development Strategy, West-East Power Transmission program promoted the construction of quite a few high dams, in which concrete arch dams have been widely employed. As we all know, the aseismic safety is crucial to high arch dams in southwest China. With the support from National Nature Science Foundation of China under Grants 50139010 and 90510018, in-depth research was conducted regarding the large-scale numerical simulation of high arch dams in strong earthquakes.
1. High arch dams may get fractured or damaged in strong earthquakes, which should be considered in its aseismic safety evaluation. As is known that concrete is inhomogeneous on the mesoscopic level, and taking advantage of this fact could better simulate the fracture process of concrete structures. However, as far as high concrete dams are concerned, it would be impossible and unnecessary to precisely simulate this inhomogeneity. If the arch dam is modeled with meshes fine enough, every mesh can be regarded as homogeneous, while the mesoscopic inhomogeneity is taken into account via random distribution of material properties of the element. In the meantime, the plasticity and anisotropism of every single element can be neglected. In the presented model for damage analysis of arch dams, elastic damage constitutive equations together with simple failure criterions, i.e., Mohr-Coulomb Principle with tension cut-off, are employed to simulate the nonlinearity of concrete. Taking the Dagangshan Arch Dam as an example, numerical result accords with results of shaking table test, which verifies the validity of the presented model. An important feature of this model is simplicity, which avails its application to large-scale computation. Last but not least important, the conversion from continuity to discontinuity can be simulated with this single model. On this basis, certain factors that affect the damage status of arch dams such as joints and radiation damping of the unbounded media are further investigated.
2. Much research work has been conducted in the field of structure-foundation interaction, but these work seldom focused on the large scale analysis of massive structures such as high arch dams. The Damping Solvent Extraction Method (DSEM) as proposed by Wolf and Song simulate radiation damping in a novel way. Artificial damping is introduced into the near field adjacent to the structure, and is extracted afterwards. Then the stiffness matrix of the unbounded media can be obtained by applying an assumption. DSEM avoided the convolution integral generally obssessing other methods and possesses the potential for application to large scale computation. However, DSEM is now only employed in 2D SSI problems, and pitifully with low computation efficiency and small capacity. By extending this model into 3D problems, together with in-depth research on the algorithm and matrix storage styles, a DSEM-based interaction model in the time domain for large scale computation of high arch dams is presented. Based on parametric study, relevant parameters are suggested:dl/b=1～1.5 and l=2～3b . Here d refers to the undimensional artificial damping, 1 is the size of the near field while b is the characteristic length of the foundation. The presented model is employed in the damage simulation of Dagangshan Arch Dam subjected to strong earthquakes. And it's observed that the damage of arch dam is greatly alleviated with the radiation damping considered.
3. With limited computational capacity for large scale finite element analysis, meshes of different sizes may be employed according to the significance of different parts of the system considered. Then techniques for transition between coarse and fine elements should be introduced. Three methods for transition are proposed, viz. the Springed Joint Method, the Master DOF (Degree of Freedom) Method and the 13-node element. The former is based on Qiang Tianchi's interface coupled method which was founded according to the least potential energy method. As in the Joint Element Method, with fictitious nodes and sub elements technique employed, the integral in Qiang Tianchi's version is simplified and transition between two sets of coordination which requires high precision is avoided. The Master DOF Method utilizes displacement constraint and needs only simple matrix operation in application. While in the 13-node element, the integration region is divided into four sub-regions, each with linear interpolating functions. All the three methods guarantee the displacement coordination between coarse elements and fine elements. Their accuracy and feasibility were verified, and the 13-node element has been employed in the damage simulation of high arch dams subjected to strong earthquakes.
4. The aseismic evaluation of high arch dams calls for large-scale and efficient numerical simulation. Personal computer, despite its rapid development, can hardly meet the needs. High performance parallel computing is the ultimate solution to this problem. A PC cluster was setup with 4 personal computers and high-speed network to be the parallel computation platform. And a parallel program PDPAD was developed for numerical simulation of damage process of high arch dams in strong earthquakes. Based on Domain Decomposition Method, the proposed damage simulation model as detailed in Chapter 2 is programmed to parallel finite element codes with MPI (Message Passing Interface) in FORTRAN 9.0 on Linux Redhat 9.0. PDPAD exhibits high scalability and speedup ratio and has the ability for large scale computation. It is employed in the damage process simulation of Dagangshan Arch Dam and can handle more than one million DOFs on the 4-node platform.
引文
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