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

我们正在进行一个基本的好奇心驱动的项目，对公共安全有直接的影响。智力上的优点在于发展了一种分析技术来模拟重力加载块体的横向无约束剪切位移。公共安全问题涉及工程兵团的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索姆的东部，容纳了超过一百万英亩英尺的水。在福尔索姆大坝和萨克拉门托市中心之间，美国河流经加州人口最稠密的地区之一。最近使用原始地表地形数据进行的计算表明，对于涉及单体独立滑动的地震场景，安全系数低得令人无法接受，在这种情况下，给定块体可能很少或没有横向约束。Co-P.I。理查德·古德曼是福尔松大坝出口改造项目外部评审小组的成员，他为我们提供了获取福尔松巨石下地表剖面现有地形数据的独特途径。这使我们能够在测试样品中近似地复制实际表面轮廓，以及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，即使可以获得两个滑动表面的完整地形信息（如福尔索姆大坝的情况）。我们正在开发一个考虑无约束边界条件的数学滑动模型，提供三维破坏（扩张）路线的预测。我们正在利用泛函的性质，并对粗糙表面进行相对简单的测试，以开发一个描述无约束滑动的基于能量的解析方程。最小化虚拟功和设置约束，反映接触点滑动的表面之间的相互作用，允许计算沿表面的每个滑动点的最低能量路径。这种方法正在扩展到可能接触点的候选集，以描述粗糙块在粗糙表面上滑动的净运动，这不是一个微不足道的问题，因为凹凸不平的接触集随着位移而变化。该方程将经过经验改进并扩展到半约束情况。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，该装置允许在基本方向上几乎不受约束的横向运动。该设备被整合到专门的声发射（AE）剪切测试设备中，该设备是为以前的NSF拨款而建造的。用于正常负载的上加载平台嵌入了24个Glaser/ nist型高保真声发射传感器，可从滑动表面的局部运动产生完整的定量时域波形。当前问题的超确定允许在三维空间中非常精确地定位源，并将源的详细运动学表示为力矩张量的反演。除了生命安全问题，更广泛的影响包括我们对无约束块的摩擦行为的进一步理解。这将为许多其他领域的研究人员提供一个工具。通过对震源运动学的声发射数据进行反演，可以获得相互作用的岩石相互作用和行为的基本知识，这对断层破裂建模和能量释放估计具有重要意义。这项工作是私家侦探的直接成果他以前的工作。除了SUPERB和CAMP项目外，pi还与伯克利的弱势工程学生中心（CUES）密切合作。我们目前正在使用伯克利边缘，以协助寻找合格的研究生提出的项目。伯克利边缘，部分由国家科学基金会资助，是一个招聘，保留和发展计划，为传统上代表性不足的少数民族研究生在科学，数学和工程。此外，P.I.直接涉及本科生的研究项目的各个方面（目前有4个），并指导具有电气工程，物理和IEOR背景的学生。这种跨学科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。

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.