Abstract The location of soil-rock interfaces (SRIs) may significantly affect the underground construction works, including the design of underground geotechnical structures. The prediction of the location of SRI using limited borehole data is a challenging task. To address this challenge, this paper presents a comparison study of four methods for spatially predicting the SRI elevation, namely the polynomial regression, spline interpolation, one-dimensional spline regression, and a Bayesian-based conditional random field. The consistencies, prediction accuracies, patterns of the predicted curves, and prediction uncertainties for various methods are evaluated. Borehole data from two sites in Singapore are used in the comparative study. The results show that the spline interpolation method produces the least consistent estimation of SRI profiles. The spline interpolation method also has lower prediction accuracies than the other three methods and cannot provide any information regarding the prediction uncertainty. The spatial trend of the geological interface cannot be captured by the polynomial regression method with a relatively high (i.e., 10) order of the polynomial when faults and folds exist. Advantages of the spline regression method over the conditional random field methods include that (i) it provides a clear and explicit spatial trend of the SRI, which well reflects the geological complexity of the sites; (ii) it avoids the cumbersome estimation of random field parametric values, which is a challenging task under the condition of limited data; and (iii) it can differentiate the zones with different prediction accuracies, which cannot be accomplished by the conditional random field method due to limited data. To sum up, the spline regression method produces a simpler and more informative curve of the SRI than the other three methods and thereby is useful as it can guide site investigations to be carried out at geologically uncertain areas to reduce risks, especially for underground construction projects

中文翻译：

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土石界面位置的比较空间预测

摘要 土石界面（SRI）的位置可能会显着影响地下施工工程，包括地下岩土结构的设计。使用有限的钻孔数据预测 SRI 的位置是一项具有挑战性的任务。为了应对这一挑战，本文对四种空间预测 SRI 高程的方法进行了比较研究，即多项式回归、样条插值、一维样条回归和基于贝叶斯的条件随机场。评估了各种方法的一致性、预测精度、预测曲线的模式和预测不确定性。新加坡两个地点的钻孔数据用于比较研究。结果表明，样条插值法产生的 SRI 分布估计的一致性最低。样条插值方法的预测精度也低于其他三种方法，并且不能提供有关预测不确定性的任何信息。当存在断层和褶皱时，具有较高（即10）阶多项式的多项式回归方法无法捕捉地质界面的空间趋势。样条回归方法相对于条件随机场方法的优点包括：(i) 它提供了清晰明确的 SRI 空间趋势，很好地反映了站点的地质复杂性；(ii) 它避免了随机场参数值的繁琐估计，这是在有限数据条件下的一项具有挑战性的任务；(iii) 它可以区分具有不同预测精度的区域，由于数据有限，这是条件随机场方法无法完成的。总而言之，样条回归方法比其他三种方法产生的 SRI 曲线更简单、信息更丰富，因此很有用，因为它可以指导在地质不确定区域进行现场调查以降低风险，特别是对于地下建筑项目