This study develops an efficient Bayesian approach using the parametric bootstrap method for characterizing the joint probability density function (PDF) of c′ and ϕ′ based on limited site-specific test data and prior knowledge. An example using real data of c′ and ϕ′ obtained from direct shear tests on alluvial fine-grained soils at the Paglia River alluvial plain in Central Italy is presented to illustrate and demonstrate the parametric bootstrap method. A sensitivity study is performed to investigate the impact of the amount of site-specific test data and prior knowledge on the posterior statistics of c′ and ϕ′. The results indicate that the parametric bootstrap method has a good accuracy and efficiency in characterizing the joint PDF of c′ and ϕ′. By reconstructing the likelihood function and rewriting the joint PDF of c′ and ϕ′ based on a large number of parametric bootstrap samples, the parametric bootstrap method significantly improves the efficiency of the conventional Bayesian approach while retaining the same accuracy as the conventional Bayesian approach. The equivalent sample pairs of c′ and ϕ′ generated using the Markov chain Monte Carlo simulation represent the joint PDF of c′ and ϕ′ well. The amount of site-specific test data and prior knowledge have a significant impact on the posterior statistics of c′ and ϕ′. Increasing the amount of the site-specific data and informativeness of the prior knowledge can reduce the statistical uncertainty in the posterior statistics. In addition, the role of prior knowledge decreases as the amount of the site-specific data increases.

这项研究基于有限的现场特定测试数据和先验知识，开发了一种有效的贝叶斯方法，使用参数化自举方法来表征c '和ϕ '的联合概率密度函数（PDF）。以意大利中部的帕格里亚河冲积平原上冲积细粒土的直接剪切试验获得的使用真实数据c ′和ϕ ′为例，以说明和证明参数引导法。进行敏感性研究以调查特定位置的测试数据和先验知识量对c ′和ϕ的后验统计的影响'。结果表明，该参数引导方法表征的联合PDF良好的精度和效率ç '和φ '。通过重构似然函数并基于大量参数自举样本重写c '和ϕ '的联合PDF ，参数自举方法可显着提高常规贝叶斯方法的效率，同时保持与常规贝叶斯方法相同的准确性。相当于样品对Ç '和φ使用马尔可夫链蒙特卡洛模拟产生的'表示的关节PDF Ç '和φ' 好。特定地点的测试数据和先验知识的数量对c '和ϕ '的后验统计有重要影响。增加特定地点数据的数量和先验知识的信息性可以减少后验统计中的统计不确定性。另外，先验知识的作用随着站点特定数据量的增加而降低。