An Unconstrained Sliding Friction Model and an Application to the Folsom Dam

无约束滑动摩擦模型及其在福尔瑟姆大坝的应用

• 批准号: 0408389
• 负责人: Steven Glaser
• 金额: $ 28.89万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-05-01 至 2008-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0408389&HistoricalAwards=false
• 关键词: Unconstrained; Sliding; Friction; Model; Application

We are undertaking a fundamental curiosity driven project that has immediate implications for public safety. The intellectual merit rests in development of an analytical technique to model laterally unconstrained shear displacement of a gravity loaded block. The public safety issue concerns safety of the Corps of Engineer's Folsom Dam. Completed in 1955, the structure is located just east of Folsom, California, and holds back over one million acre-feet of water. Between Folsom Dam and downtown Sacramento, the American River flows through one of the most densely populated regions in California. Recent calculations made with original surface topographic data have produced some unacceptably low factors of safety for seismic scenarios involving independent sliding of the monoliths, in which case there might be little or no lateral constraint on a given block. Co-P.I. Richard Goodman is a member of the Folsom Dam Outlets Modification Project external review panel, giving us unique access to existing topographic data on surface profiles beneath the Folsom monoliths. This enables us to approximately duplicate actual surface profiles in test samples, as well as to use the topographic data to analytically estimate the stability of the dam.There is currently no general analytical model for laterally unconstrained sliding, even if full topographic information is available for the entirety of both sliding surfaces (as in the case of Folsom Dam). We are developing a mathematical sliding model that takes into account the unconstrained boundary conditions, offering a prediction of the 3-D failure (dilation) route. We are utilizing the properties of functionals and examining relatively simple tests on rough surfaces to develop an analytic energy-based equation describing unconstrained sliding. Minimizing virtual work and setting constraints which reflect the interaction of the surfaces between which contact points are sliding allows the calculation of the lowest energy path of each sliding point along the surface. This methodology is being extended over the candidate set of likely contact points to describe the net motion of a rough block sliding over a rough surface, which is not a trivial problem because the contacting set of asperities changes with displacement. The equation will be empirically refined and extended to the semi-constrained case.Experimental verification of the proposed model is being carried out using a simple but entirely new device, which allows virtually unconstrained lateral motions in the principle directions. This device is being incorporated into the specialized acoustic emission (AE) shear testing facility built for a previous NSF grant. The upper loading platen for the normal load has embedded within 24 Glaser/NIST-type high-fidelity AE sensors which yields full quantitative time-domain waveforms from local movements on the sliding surfaces. The overdetermination of the present problem allows for extremely accurate source location in 3-D space and inversion for the detailed source kinematics expressed as a moment tensor.Besides the life safety issues, broader impacts include the furthering of our understanding of frictional behavior of unconstrained blocks. This will provide a tool for many other researchers in a variety of fields. Basic knowledge of the interaction and behaviors of interacting asperities will grow out of the inversion of AE data for source kinematics, which has important implications for fault rupture modeling and energy release estimates. This work is a direct outgrowth of the P.I.'s previous work.The P.I. works closely with Berkeley's Center for Underrepresented Engineering Students (CUES), in addition to the SUPERB and CAMP programs. We are presently using the Berkeley Edge to assist in finding qualified graduate students for the proposed project. The Berkeley Edge, partially funded by the National Science Foundation, is a recruitment, retention, and advancement program for traditionally underrepresented minority graduate students in science, mathematics, and engineering. In addition, the P.I. directly involves undergraduate students in all aspects of his research program (4 currently), and supervises students with backgrounds in electrical engineering, physics, and IEOR. This interdisciplinearity forces all the students to grow technically and to respect other disciplines and ways of approaching problems.

我们正在进行一个由好奇心驱动的基本项目，该项目对公共安全具有直接影响。智力上的优点在于开发了一种分析技术来模拟重力载荷下块体的横向无约束剪切位移。公共安全问题关系到工兵团福尔索姆大坝的安全。该建筑于1955年完工，位于加利福尼亚州福尔瑟姆以东，挡住了100多万英亩英尺的水。在福尔瑟姆大坝和萨克拉门托市中心之间，美洲河流经加州人口最稠密的地区之一。最近用原始地表地形数据进行的计算得出，对于涉及整体独立滑动的地震情景，安全系数低得令人无法接受，在这种情况下，对给定区块的横向约束可能很少或没有。共同P.I.理查德·古德曼是福尔瑟姆大坝奥特莱斯改造项目外部审查小组的成员，他为我们提供了独一无二的访问福尔瑟姆巨石下表面轮廓的现有地形数据。这使我们能够近似复制测试样本中的实际表面轮廓，并使用地形数据来分析估计大坝的稳定性。目前还没有横向无约束滑动的通用分析模型，即使两个滑动面的全部地形信息都可用(如Folsom大坝的情况)。我们正在开发一个数学滑动模型，该模型考虑了无约束的边界条件，提供了对三维破坏(膨胀)路线的预测。我们正在利用泛函的性质和对粗糙表面的相对简单的测试来开发一个描述无约束滑动的基于能量的解析方程。最小化虚功并设置反映接触点在其之间滑动的表面的相互作用的约束允许计算沿该表面的每个滑动点的最低能量路径。这种方法被推广到候选的可能接触点集合上，以描述在粗糙表面上滑动的粗糙块的净运动，这不是一个微不足道的问题，因为接触的粗糙集随着位移而变化。该方程将被经验修正并推广到半约束情况。正在使用一种简单但全新的装置对所提出的模型进行实验验证，该装置允许在主要方向上几乎不受约束的横向运动。该设备将被整合到专门的声发射(AE)剪切测试设施中，该测试设施是为之前的NSF拨款而建造的。用于法向载荷的上加载压板嵌入了24个Gaser/NIST型高保真声发射传感器，该传感器可根据滑动表面上的局部运动生成完整的量化时域波形。对当前问题的过度确定允许在3-D空间中进行极其精确的震源定位和以矩张量表示的详细震源运动学的反演。除了生命安全问题，更广泛的影响包括加深我们对无约束块体摩擦行为的理解。这将为各个领域的许多其他研究人员提供工具。声发射数据对震源运动学的反演将产生相互作用和相互作用的凹凸体行为的基本知识，这对断层破裂模拟和能量释放估计具有重要意义。这项工作是P.I.S之前工作的直接产物。P.I.除了卓越的和夏令营项目外，还与伯克利的代表不足工程学生中心(CUES)密切合作。我们目前正在使用伯克利边缘来帮助为拟议的项目寻找合格的研究生。伯克利边缘计划由国家科学基金会提供部分资金，是一项面向科学、数学和工程领域传统上代表性较低的少数族裔研究生的招聘、保留和晋升计划。此外，P.I.直接让本科生参与他的研究项目的所有方面(目前有4名)，并指导具有电气工程、物理和IEOR背景的学生。这种跨学科性迫使所有学生在技术上成长，并尊重其他学科和解决问题的方法。