摘要
可靠度理论在结构工程中应用较为广泛,但是在岩土工程中可靠度理论的研究工作却开展得相对较少。这主要是因为岩土工程中不确定性因素很多。本文以多桩型复合地基为对象,对岩土工程可靠度理论及应用进行了研究。
首先,本文对可靠度分析的基本理论做了研究。提出确定β分布各参数的经验公式简化迭代过程,有效处理了随机变量分布范围的估计问题,同时首次将β分布函数引入到模糊失效事件的隶属函数中,使得隶属函数在整个定义域上具有光滑、曲线中心对称性的特点。对于功能函数较简单的情况,本文推导出计算模糊事件失效概率的具体表达式。针对现有一次二阶矩法进行可靠性指标求解时其收敛性不能得到保证的缺点,本文提出一个等步长迭代法修正一次二阶矩法,并证明了其收敛性,从而增大了一次二阶矩法求解可靠性指标的应用范围。
其次,本文给出了一个计算多桩型复合地基面积置换率的可靠性设计方法。应用概率、统计学理论,引入一个随机变量作为搅拌不均匀因子,定量分析搅拌不均匀性对水泥土无侧限强度以及深层搅拌桩桩身强度带来的影响,分别得出该因子在传统设计和可靠度分析中的应用。在土体选用双折线弹塑性本构模型、莫尔-库伦屈服准则、相适应流动法则的情况下,对多桩型复合地基分别进行了地基承载力和沉降可靠度分析。得出面积置换率与可靠性指标之间的关系,使得面积置换率的确定更为合理。
Due to the uncertainty of soil properties, reliability theory, which has been widely used in structural engineering, has been seldom applied in geotechnical engineering. In this thesis, some reliability-related problems in geotechnical engineering are studied with multi-pile composite foundation as main target.
Firstly, the basic theory of reliability analysis is studied. An iteration process to determine the parameters for a beta probability density function and an empirical equation to simplify this iteration are presented. As a result, the estimation of the bounds of random variables is efficiently made. Furthermore, beta distribution function is introduced to determine the membership function of a fuzzy failure event for the first time. Therefore, the membership function is smooth within its domain, and is characterized by center symmetry. By utilizing the character of performance functions which are relatively simple in geotechnical problems, an explicit formula to estimate the fuzzy failure probability is derived. In order to overcome the disadvantage that the convergence of First Order-Second Moment (FOSM) method is not guaranteed, this thesis proposes an Equal Step Iteration Method (ESIM), of which the convergence is proved as well.
Secondly, a Reliability-Based Design (RBD) methodology is presented to determine the replacement ratio (percent coverage) of piles in a multi-pile composite foundation. Based on the probabilistic and statistic theory, a random variable, denoted as the factor of deep soil mixing quality, is proposed to quantitatively assess the influences of mixing quality on the strengths of cemented soil and pile shaft. Furthermore, the applications of this random variable in conventional designs and RBD method are analysed. In this study, the reliability of bearing capacity and settlement of multi-pile composite foundation are analyzed when the characteristics of soil are adopted as Mohr-Coulomb’s shear yield criterion, associated flow rule and bilinear elasto-plastic model for stress-strain relationship. According to the relationship between the reliability index and the replacement ratio of piles, the replacement ratios of multi-pile composite foundation can be evaluated in a rational manner.
引文
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