The predicted performance of a geotechnical system may deviate from the in situ observation due to the uncertainties in the input geotechnical parameters, solution model, and observation error. A precise characterization of these uncertainties is a significant challenge primarily because of limited data availability. The Bayesian theory provides a means for updating these uncertainties by incorporating prior statistical information and observations. However, conventional Bayesian inference focuses on limited sources of uncertainties. This paper presents a probabilistic back analysis method for improved reliability of subsequent predictions that considers all the uncertainties. Three distinct features of this new method include: (1) multiple observations are incorporated into the Bayesian updating, (2) the statistical information of the uncertain variables is updated in a stage-by-stage manner, and (3) the posterior distributions of uncertain variables are derived with Markov Chain Monte Carlo (MCMC) simulation that is based on the Hamiltonian Monte Carlo (HMC) algorithm. Two case histories, including a braced excavation problem and a tunnel excavation problem, are analyzed to demonstrate the effectiveness of the new method. The advantages of this new back analysis method over the conventional Bayesian updating analyses are documented.

岩土工程系统的预测性能可能会偏离原位由于输入岩土工程参数、求解模型和观测误差的不确定性而导致的观测。这些不确定性的精确表征是一项重大挑战，主要是因为数据可用性有限。贝叶斯理论提供了一种通过结合先前的统计信息和观察来更新这些不确定性的方法。然而，传统的贝叶斯推理侧重于有限的不确定性来源。本文提出了一种概率反分析方法，以提高后续预测的可靠性，同时考虑所有不确定性。这种新方法的三个显着特点包括：(1) 将多个观测值纳入贝叶斯更新，(2) 不确定变量的统计信息逐步更新，(3) 不确定变量的后验分布是通过基于哈密顿蒙特卡罗 (HMC) 算法的马尔可夫链蒙特卡罗 (MCMC) 模拟得出的。分析了两个案例历史，包括支撑开挖问题和隧道开挖问题，以证明新方法的有效性。这种新的反向分析方法相对于传统的贝叶斯更新分析的优势被记录在案。