Canadian Geotechnical Journal, Ahead of Print.
This paper develops a hierarchical Bayesian model (HBM) that integrates the physical knowledge and the test data to predict the small-strain shear modulus Gmax for a target sand type. The limited target-specific data are combined with the abundant generic data through a hierarchical structure so that the variability of Gmax within one sand type and across different sand types can be captured. The hyperparameters that characterize the same underlying distribution of physical model parameters across all the sand types are first estimated from the abundant generic data. The model parameters for the new sand type are then updated as the limited site-specific data become available. The approach is illustrated using a generic database and two real examples not covered by the generic database. Multiple possible hierarchical models are compared in terms of model complexity and goodness-of-fit. The results show that the hierarchical modeling of small-strain shear modulus data is reasonable and necessary. The hierarchical model can provide less biased and more accurate predictions of Gmax compared to the commonly used complete pooling model, especially in cases where the site-specific data are quite different from the overall average of the generic database.

中文翻译：

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预测砂小应变刚度的分层贝叶斯模型

加拿大岩土工程杂志，印刷前。
本文开发了一种分层贝叶斯模型（HBM），该模型集成了物理知识和测试数据来预测目标砂类型的小应变剪切模量 Gmax。有限的特定目标数据通过分层结构与丰富的通用数据相结合，以便可以捕获一种砂类型内和不同砂类型之间的 Gmax 变化。首先根据丰富的通用数据来估计表征所有砂类型的物理模型参数的相同基本分布的超参数。当有限的特定地点数据可用时，新砂类型的模型参数就会更新。使用通用数据库和通用数据库未涵盖的两个真实示例来说明该方法。在模型复杂性和拟合优度方面比较了多种可能的分层模型。结果表明，小应变剪切模量数据的分层建模是合理和必要的。与常用的完全池化模型相比，分层模型可以提供偏差更小、更准确的 Gmax 预测，特别是在特定站点数据与通用数据库的总体平均值有很大差异的情况下。