基础设计中的可靠度评估

Reliability assessments on foundation design

阐述基于可靠度理论的基础设计的评估。首先总结具有结构抗力和荷载效应2个基础变量的结构可靠度基本理论。结构抗力的不确定性可以由统计学上的平均值和变异系数(cov或Ω)来描述。变异系数指变量的标准差和平均值的比值。敏感度分析的结果显示结构抗力的变异系数(Ω)R在其应用范围之内时,在分析结构可靠度方面扮演着相当重要的角色。基于这些阐述,在预先指定的风险水平(pf)上ΩR一定有其上限。当结构抗力呈正态分布的时候,这个极限ΩR独立于荷载效应随机性,和安全指数β成反比。安全指数可以定义为在标准正态分布区间极限状态到原点之间的最小距离。在这个极限ΩR之下,结构可以在预定风险水平之下安全工作。中心安全系数(FS)可以由结构抗力和荷载效应的变异系数根据平方关系求得。然而,一些情况下结构抗力为非正态分布的情况并不少见。因此,等效正态分布的概念可以用来得到非正态分布结构抗力的ΩR极限。地质方面的随机变量可能是正态分布,也可能是非正态分布,结构抗力中基本变量之间的关系可能是线性也可能是非线性,或者非常复杂以致于结构抗力只能通过有限元分析才能得到。在此情况下,随机数可以通过蒙特卡洛模拟技术获得。拟合的结构抗力的分布可以在随机试验的基础上通过配合度检验确定。现实中,土壤的力学特性不是各向同性的,同样也不能认为是单一材料的,它们的不确定性是不可以被忽略的。简便的设计方式认为不确定参数是常数,并且通过使用定值的安全系数来确定结构截面,设计原则没有将土壤参数对安全系数的影响考虑进去。参考计算出来的失效概率表明,确定值的安全系数法无法保证足够的安全。因此,在某种情况下,安全系数大于等于3,对于结构容许承受能力,并不能认为太保守。

The basic concepts of the structural reliability are summarized in terms of two normally basic variables, i.e. structural resistance and load effect. The uncertainty in structural resistance could be statistically characterized by mean and coefficient of variation （coy or ΩR） which is defined as the ratio of its standard deviation to its mean. The result of sensitivity analysis reveals that when the coefficient of variation （ΩR） is within its application scope, it will play a rather important role in structure reliability analysis. Based on these formulations, there must be an upper limit of ΩR for the pre-specified acceptable level of risk （pf）. The increment of coefficient of variation of load effect （Ωs） shows a minor influence on the central factor of safety （Fs） and its effect diminishes rapidly where ΩR approaches the upper limit. Below this limit, the structural system could be used safely for a prespecified target reliability. For lower value of ΩR, the target Fs could be determined from the quadratic relationship between ΩR and Ωs. The structural resistance for foundations is typically functioning of soil properties, sections and dimensions. It is not uncommon that uncertainties in soil properties could be normal or non-normal distribution and the relationship among basic variables in forming the structural resistance could be either non-linear or so complicated that results could be obtained from finite element analyses only. Fortunately, the randomness of structural resistance could be obtained by Monte Carlo Simulation Technique. Then the fitted distribution of outcome experiments could be specified by Goodness-of-Fitted Tests. The applicability of proposed concepts could be demonstrated in numerical examples, e.g. driven pile, spread footing, bored pile and laterally loaded pile. For the conventional design approach, soil parameters are considered to be constant. The solution is simplified through the use of deterministic safety factor. In reality, soil is neither isotropic nor homogeneous such that their uncertainties could not be ignored. References to the calculated failure probability evidence that the deterministic safety factor could not guarantee enough safety. In some cases, an Fs of 3 or more is not considered too conservative to apply for the structural resistance.