基于Copula函数的CFG桩复合地基载荷-变形曲线的概率分析

CFG桩(cement-fly ash-gravel pile)复合地基是一种重要的地基处理形式，在日益增加的大面积住宅和商业开发中作用越来越突出，然而该种桩型的加卸荷-沉降变形特性仍然需深入研究，尤其在概率评估方面。根据北京星光影视股份有限公司生产科研基地项目工地中的21根CFG桩单桩静载试验和32个复合地基静载试验的原位加卸载测试成果，采用两参数的双曲线或幂曲线回归拟合了每一条加荷-变形曲线。由于土体的内在各向异性和其强度的变异性，评估整个场地的加荷-变形曲线时，其回归参数表现出了较大的离散性。将一个场地的多组回归参数组成一个随机向量，其加载-位移曲线的不确定性可由简单的两变量随机向量体现，引入双变量联结函数（Copula）描述随机回归参数间的相依性。最后，考虑正常使用极限状态，采用基于Copula函数的模拟模型计算了CFG桩复合地基的可靠度指标。研究结果有助于改进CFG桩复合地基的概率设计与评估。

Copula-based analysis of load-displacement curves of cement-fly ash-gravel pile

CFG pile(cement-fly ash-gravel pile) is an important type of ground improvement, and its role is becoming even more prominent as more accessible soft foundations become increasingly exploited by the surging urban industrial development in China. Yet despite its significance, the load-settlement behaviour is poorly understood on this pile type; particularly in the context of probabilistic assessments. Based on a series of repeating full-scale field load tests for CFG piles (21 samples) and the pile-soil intermediates(PSI) or composite foundation systems (32 samples) under static axial compression loading, the data of the loading-displacement curves were gathered from a field site in Beijing city. A regression curve is facilitated by approximating the load-settlement curve for each load test using a two-parameter, hyperbolic or power law curve-fitting equation. Moreover, when assessing the regression parameter values from entire pile load measurements across the test site, the scatter in load-displacement curves attributed to inherent soil variability can be found. Thus, the uncertainties of the load-displacement curves at the site are represented by a relatively simple bivariate random vector containing the regression parameters as its components. A bivariate Copula-based mixed distribution is further applied to capture the dependence characteristics between these regression parameters. For the CFG pile, the Pearson correlation coefficient between the power-law regression parameters is calculated to be -0.621; and the best-fitting Copula is identified as normal through the Akaike information criterion(AIC). In the case of PSI, the correlation coefficient of the regression parameters is -0.645 and their dependence structures are best described by the normal Copula. Finally, a simple Copula-based simulation model(CBSM) is used to estimate the reliability index at any specific allowable settlement for the serviceability limit state(SLS) design. The effect of the various Copulas on the reliability indexes is clarified. These analyses of the load-displacement behaviour give an insight into the probabilistic design and safety assessment of the CFG pile foundation.