Abstract Cone penetration test (CPT) is one of the most commonly used in-situ methods for characterizing spatial variability of soil properties in geotechnical site characterization. It provides almost continuous soil responses when a cone is pushed into the ground at a constant rate. With the almost continuous CPT data, many geotechnical and geological engineering problems, such as evaluation of liquefaction potential and subsurface soil stratification, may be properly addressed. Although CPT provides almost continuous soil responses along the depth direction, the number of CPT soundings along a horizontal direction is usually small for a specific site, due to time, resources, or technical constraints. In these cases, interpolation or stochastic simulations are often needed to estimate CPT data at un-sampled locations. Several methods have been developed to address this issue, such as random field approach, geo-statistical methods, among others. However, determination of the parameters needed in random field theory and geo-statistical methods often requires a relatively large number of CPT soundings along horizontal directions, which is often not available in practice. Moreover, subsurface soils often contain multiple soil layers with spatially varying and unknown layer boundaries, and therefore CPT data are often non-stationary, leading to the difficulty in dealing with non-stationary CPT data due to different soil layers. This paper proposes a new and fast method that combines Bayesian compressive sensing with Markov Chain Monte Carlo (MCMC) simulation. The proposed method is data-driven, non-parametric, and directly applicable to non-stationary CPT data without pre-stratification of subsurface soils. In addition, to improve computational efficiency of MCMC simulation, a sequential updating technique is developed using Kronecker product. Both numerical and real-life examples are used to illustrate the proposed method. The results show that the proposed method is robust and performs well.

中文翻译：

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使用马尔可夫链蒙特卡罗模拟，无需预先分层即可对二维多层锥体穿透测试 (CPT) 数据进行快速非参数模拟

摘要 锥入度试验 (CPT) 是在岩土工程场地表征中表征土壤性质空间变异性的最常用的原位方法之一。当锥体以恒定速率推入地面时，它提供几乎连续的土壤响应。有了几乎连续的 CPT 数据，许多岩土和地质工程问题，如液化潜力评估和地下土壤分层，可以得到妥善解决。尽管 CPT 沿深度方向提供几乎连续的土壤响应，但由于时间、资源或技术限制，对于特定站点，沿水平方向的 CPT 测深次数通常很少。在这些情况下，通常需要插值或随机模拟来估计未采样位置的 CPT 数据。已经开发了几种方法来解决这个问题，例如随机场方法、地统计方法等。然而，确定随机场理论和地统计方法所需的参数通常需要沿水平方向进行相对大量的 CPT 测深，这在实践中往往不可用。此外，地下土壤通常包含多个空间变化且层边界未知的土层，因此CPT数据往往是非平稳的，导致由于不同土层而导致处理非平稳CPT数据的困难。本文提出了一种新的、快速的方法，将贝叶斯压缩感知与马尔可夫链蒙特卡罗 (MCMC) 模拟相结合。所提出的方法是数据驱动的、非参数的、直接适用于非平稳 CPT 数据，无需对地下土壤进行预分层。此外，为了提高 MCMC 仿真的计算效率，使用 Kronecker 产品开发了一种顺序更新技术。数值和现实生活中的例子都被用来说明所提出的方法。结果表明，所提出的方法具有鲁棒性和良好的性能。