考虑经验模型不确定性的基坑开挖贝叶斯更新

Bayesian updating of excavation considering model uncertainty

基坑开挖工程中,最大地表沉降的预测及其失效概率的评估一直是工程师所关心的关键问题。以往在利用经验模型对最大地表沉降进行预测时,模型误差通常被忽略或者视为常数,与实际情况不符。本文提出了一种能够考虑经验模型不确定性的贝叶斯更新方法,将模型偏差系数视为随机变量,并利用现场观测数据对其进行不断更新,更新结果可用于后续阶段的基坑开挖最大地表沉降和失效概率的预测。以台北TNEC基坑开挖为例,将所提方法应用于Peck模型、Ou模型、KJHH模型等3种经验模型。结果表明:3种模型一般都会高估最大地表沉降,其中Peck模型偏差最大,KJHH模型次之,Ou模型最小,而KJHH模型偏差比Ou模型的变异性更小,通过所提方法可以有效考虑模型不确定性的影响;随着开挖的进行,基于KJHH模型的计算结果相比其它2个模型更加准确;在所研究的算例中,监测数据随着开挖的进行而增加,使得模型偏差系数和土体参数的不确定性降低,最终导致基坑失效概率的降低。

During the excavation,the prediction of maximum ground settlement and the assessment of failure probability are always concerned by engineers. Previous studies that adopt the empirical model to predict the maximum ground settlement usually ignored the model error or considered it as a constant,which was inconsistent with the actual situation. This paper proposes a Bayesian updating approach to consider the model uncertainty of an empirical model. The model bias factor is considered as a random variable and updated with field observations during the excavation. The updated results can be used to predict the maximum ground settlement and failure probability in subsequent stages. Through the TNEC excavation case study,the proposed method is applied to three empirical models,namely the Peck model,Ou model,and KJHH model. Results indicate that all the three models would overestimate the maximum ground settlement,among which the Peck model is the most biased one,followed by Ou model and KJHH model. The variability of model bias factor of KJHH model is smaller than that of Ou model. The effect of model uncertainty can be properly considered using the proposed Bayesian method. As the excavation proceeds,the KJHH model performs better than the other two models,and the failure probability of the project decreases. The latter is because uncertainties in model bias factor and soil properties reduce when more and more field observations are introduced.