报告题目：失落的宝藏：布辛内斯克的土压力理论
报 告 人：K.T.Chau (Department of Earth and Environmental Sciences,The Chinese University of Hong Kong)
A Lost Treasure:Boussinesq’s Earth Pressure Theory
报告时间：2025年3月17日（星期一）上午10:30—11:30
报告地点：7号楼7201会议室
主办单位：土木与交通学院
报告人介绍：
Professor K.T.Chau(周锦添教授)has been an adjunct professor at the Department of Earth and Environmental Sciences, Chinese University of Hong Kong, since 2020. Previously, he was Chair Professor of Geotechnical Engineering and Associate Head of the Department of Civil and Structural Engineering at Hong Kong Polytechnic University, where he also served as Associate Dean of the Faculty of Construction and Land Use (now the Faculty of Construction and Environment). He holds a Senior Diploma and Honours Diploma (with distinction) in Civil Engineering from Hong Kong Baptist College (now Hong Kong Baptist University), a Master’s degree in Structural Engineering from the Asian Institute of Technology (AIT) Thailand (recipient of the Tim Kendall Memorial Prize), and a Ph.D. in Theoretical and Applied Mechanics from Northwestern University, USA.
Professor Chau is a Fellow of the Hong Kong Institution of Engineers (HKIE). He has held prominent roles internationally, including Chairman of the Elasticity Committee of ASCE’s Engineering Mechanics Institute and Chairman of the Geomechanics Committee of ASME. His research spans applied mechanics, earthquake engineering, geomechanics, landslides, debris flows, and tsunamis. He has published over 120 journal papers and three books on geomechanics and differential equations. Recognized as one of the “World’s Top 2% Scientists” by Stanford University in 2021, 2022, and 2023, he was also inducted into the AIT Hall of Fame in 2019.
周锦添教授（Professor K.T.Chau）现为香港中文大学地球与环境科学系兼职教授（2020年起），曾任是香港理工大学土力工程讲座教授及土木及结构工程学系副系主任、建设及环境学院副院长。他获得了香港浸会学院（现为香港浸会大学）土木工程高级文凭和荣誉文凭（优异成绩），泰国亚洲理工学院（AIT）结构工程硕士学位（荣获Tim Kendall纪念奖），以及美国西北大学理论与应用力学博士学位。
周教授是香港工程师学会（HKIE）的资深会员。他在国际上担任过多个重要职位，包括美国土木工程师学会（ASCE）工程力学学会弹性力学委员会主席以及美国机械工程师学会（ASME）岩土力学委员会主席。他的研究领域涵盖应用力学、地震工程、岩土力学、滑坡、泥石流和海啸等。他发表了超过120篇期刊论文，并出版了叁本对于岩土力学和微分方程的书籍。周教授在2021年、2022年和2023年被斯坦福大学评为“全球前2%顶尖科学家”，并于2019年入选亚洲理工学院名人堂。
报告摘要：
Rankine’s and Coulomb’s theories on earth pressure are classical methods being taught at universities, and are used daily in retaining wall design. However, according to the review article “Landmarks on Early Soil Mechanics” by the late Professor Skempton (1979), Boussinesq’s (1885) formula on earth pressure coefficient actuallyoutperformed both Rankine’s and Coulomb’s theories when they are compared to the well-accepted numerical results by Caquot and Kerisel (1948). Surprisingly, even with Skempton’s favorable comment on Boussinesq (1885) theory, it remains relatively unknown. It is a lost treasure in the academic world and practicing world. No proof on Boussinesq’s elegant formula can be found in the English literature (including Skempton’s paper). In this presentation, we will present a complete proof of this lost treasure. This new solution satisfies both the equilibrium equation and yield condition, subjected to both free ground surface condition and frictional contact condition on the retaining wall. Boussinesqfound that a “Rankine yielding wedge” (satisfying the Mohr-Coulomb criterion) closeto the ground surface and a homogenous soil wedge close to the retaining wall (subjecting to gravity and an unknown stress field modeled by a stress function). In view of the surface stress-free boundary condition and the frictional contact boundary condition on the wall, these unknown stress functions are found identically zero in the Rankine wedge but alinear function of the distance from the top of the retaining wall in the homogeneous wedge. To the first order of approximation, the yielding condition leads to a 1-D hyperbolic equation(wave equation) for the stress function. Subsequently, the method of characteristics can be applied to find a closed-form solution for the stress field after integration. In turn, a closed-form elegant formula can be found for the earth pressure coefficient, which is more accurate than Coulomb’s theory (as shown by Skempton). My aim is to popularize this long-forgotten elegant and accurate formula (a lost treasure discovered by Skempton), and, hopefully, it will be one day taught worldwide by academics and used by practicing engineers.
朗肯（Rankine）和库仑（Coulomb）的土压力理论是经典方法，当前在大学中被广泛教授，并且在挡土墙设计中被日常使用。然而，根据已故斯凯普顿教授（Professor Skempton）在1979年发表的综述文章《土力学早期的里程碑》（Landmarks on Early Soil Mechanics），当朗肯和库仑的理论与Caquot和Kerisel（1948年）公认的数值结果相比时，布辛内斯克（Boussinesq）在1885年提出的土压力系数公式实际上表现得更为出色。令人惊讶的是，即使斯凯普顿对布辛内斯克（1885年）理论给予了高度评价，它仍然鲜为人知，成为学术界和工程实践中的一项失落的宝藏。对于布辛内斯克优雅公式的证明，在英文文献中（包括斯凯普顿的文章）都无法找到。在本次报告中，我们将完整地证明这一失落的宝藏。这一新解不仅满足平衡方程和屈服条件，还同时满足自由地表条件和挡土墙上的摩擦接触条件。布辛内斯克发现，一个接近地表的“朗肯屈服楔体”（满足莫尔—库仑准则）和一个靠近挡土墙的均质土楔体（受到重力作用且具有一个未知的由应力函数建模的应力场）构成了解的基础。鉴于地表无应力边界条件和挡土墙上的摩擦接触边界条件，这些未知的应力函数在朗肯楔体中恒为零，而在均质楔体中则是与挡土墙顶部距离成线性关系的函数。在一阶近似下，屈服条件导致应力函数满足一维双曲方程（波动方程）。随后，通过特征线方法进行积分，可以求得应力场的闭合解。由此，可以得出一个优雅的土压力系数闭合公式，其准确性优于库仑理论（如斯凯普顿所示）。这一长久被遗忘的优雅且准确的公式（斯凯普顿发现的失落宝藏）的推广，希望能被全球的学者教授并被工程师在实践中广泛应用。