张 伟,田新然
AuthorsHTML:张 伟，田新然
AuthorsListE:Zhang Wei,Tian Xinran
AuthorsHTMLE:Zhang Wei，Tian Xinran
Unit:天津大学建筑工程学院，天津 300072
Unit_EngLish:School of Civil Engineering，Tianjin University，Tianjin 300072，China
Abstract_Chinese:筒形基础广泛应用于海洋平台，但由于海洋复杂的环境和筒形基础特殊的结构形式，传统的地基承载力理 论难以准确分析筒形基础的竖向极限承载力．为了解决这一问题，将突变理论引入承载力的计算中，分别采用突变 理论的理论方法和经验方法进行求解．理论方法通过严谨的物理阐释和数学推导，直接得出系统的总势能表达式， 并通过一系列的数学变换得到基于筒基总势能的尖点突变模型，求出临界失稳点和其对应的极限承载力．经验方法 分别以筒基位移、土体塑性应变、等效应力、系统应变能作为突变判据，建立了加载系数和突变判据的突变模型， 利用 ANSYS 的数值计算结果反演出系统的势函数，并通过建立模型的标准势函数来计算相对应的控制变量和分叉 集，由此判断系统是否发生突变，从而得出发生突变时候的极限承载力．通过对 5 种不同尺寸的模型进行分析计算 表明，理论方法由于总势能函数难以精确推导，其计算结果与常用的理论公式误差较大．而经验方法弥补了理论方 法的不足，基于 4 种突变判据的计算结果与其他理论公式的拟合度较高，同时与理论公式相比，突变理论的经验方 法无需考虑海洋环境、筒体和土体参数等因素的影响，只需将数值模拟的结果带入突变理论模型，即可得出相应的 地基极限承载力．
Abstract_English:Bucket foundations have been widely used in offshore platforms. Due to the complex marine environment and the special structural form of bucket foundations，traditional bearing capacity theory could not be used to evaluate the vertical bearing capacity of bucket foundations accurately. In order to solve this problem，catastrophe theory was introduced to the calculation of bearing capacity. The theoretical and the empirical methods of catastrophe theory were used respectively. In the theoretical method，the total potential energy function of the system was obtained directly by rigorous physical interpretation and mathematical derivation. After a series of mathematical transformations，the critical instability point and its corresponding bearing capacity were obtained by deducing the cusp catastrophe model on the basis of total potential energy of the bucket foundations. The empirical method utilized the displacement of bucket foundations，plastic strain of soil，equivalent stress and system strain energy as the criteria of catastrophe，and then established the catastrophe model on the basis of loading coefficient and the criterion of catastrophe. Numerical computation results of ANSYS were used to derive the inverse of potential function. Moreover，the corresponding control variable and the set of divarications were calculated by establishing the modelof standard potential function. Therefore，whether there was a catastrophe and the corresponding bearing capacity could be judged. Through the analysis and calculation of the five models with different sizes，it is shown that the total potential energy function of the theoretical method is difficult to derive accurately，and the difference between the calculation result and the commonly used theoretical formula is large. However，the empirical method makes up for the deficiency of the theoretical method，and the results based on the four criteria of catastrophe fit better with the other theoretical formula. Compared with the theoretical formula，the empirical method of catastrophe theory does not need to consider the influence of complex marine environment，bucket and soil parameters and other factors. Therefore，the corresponding ultimate bearing capacity of foundations can be obtained only by substituting the numerical simulation results into the catastrophe theoretical model.
Keyword_Chinese:突变理论；理论方法；经验方法；突变判据
Keywords_English:catastrophe theory；theoretical method；empirical method；criterion of catastrophe

PDF全文下载地址:http://xbzrb.tju.edu.cn/#/digest?ArticleID=6652