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<p>With the advancement of infrastructure reconstruction and expansion projects, the problem of uneven settlement of old and new subgrades has become a key challenge that restricts the safety and service performance of the project. Conventional borehole sampling often perturbs the material and sparsely covers the domain, making spatial variability—especially anisotropy—difficult to characterize reliably. However, the existing numerical simulation and empirical formula are limited by idealized assumptions or parameter uncertainties, which cannot effectively quantify the non-stationary variation law under complex geological conditions. Therefore, based on the expansion project of Lianhuai Expressway, this paper proposes a soil spatial variation quantization method that combines two-dimensional Bayesian compressed sensing (BCS) and discrete cosine transform (DCT) basis functions. Based on the piezocone penetration tests (CPTU) in situ test data, the efficient reconstruction and cross-scale variation analysis of over-consolidation ratio (OCR), undrained shear strength (<i>S</i><sub><i>u</i></sub>), and compression modulus (<i>E</i><sub><i>s</i></sub>) parameter fields are realized by trend term separation, DCT sparse reconstruction, and autocorrelation function (ACF) analysis. Results indicate laterally coherent fields with depth-dependent strengthening after detrending and DCT–BCS reconstruction. Inversions of OCR, Su, and <i>Es</i> are consistent with CPTU correlations and capture the differences between the old and new subgrades. The uncertainty analysis of DCT spectrum further shows that the standard deviation (SD) in the low-frequency component is significantly higher than that in the high-frequency component, which verifies the stability of the reconstruction results. The proposed BCS–DCT framework reconstructs spatial fields from sparse, anisotropic CPTU measurements and characterizes their autocorrelation. It complements kriging/GP models by providing ACF-based correlation length diagnostics and posterior uncertainty that aid interpretation. On a representative data set, the ACF inferred by BCS–DCT agrees with that derived from a semivariogram, indicating reliable correlation scales. It provides high-precision and high-efficiency technical support for foundation performance evaluation and differential settlement control in road expansion projects.</p>

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Similarity study of soil spatial variability between the longitudinal sections of new and old subgrade foundations based on the autocorrelation function of CPTU test

  • 期刊论文

  • 发表日期：

    2026年2月27日

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  • Caijin Wang,
  • Shuai Zhu,
  • Liangfu Xie,
  • Annan Zhou,
  • Hongjian Zhang,
  • Jingtong He,
  • Zhiyi Jin,
  • Guojun Cai,
  • Xuejun Liu,
  • Xueling Hu,
  • Tao Zhang,
  • Songyu Liu,
  • Zhiming Liu

摘要

With the advancement of infrastructure reconstruction and expansion projects, the problem of uneven settlement of old and new subgrades has become a key challenge that restricts the safety and service performance of the project. Conventional borehole sampling often perturbs the material and sparsely covers the domain, making spatial variability—especially anisotropy—difficult to characterize reliably. However, the existing numerical simulation and empirical formula are limited by idealized assumptions or parameter uncertainties, which cannot effectively quantify the non-stationary variation law under complex geological conditions. Therefore, based on the expansion project of Lianhuai Expressway, this paper proposes a soil spatial variation quantization method that combines two-dimensional Bayesian compressed sensing (BCS) and discrete cosine transform (DCT) basis functions. Based on the piezocone penetration tests (CPTU) in situ test data, the efficient reconstruction and cross-scale variation analysis of over-consolidation ratio (OCR), undrained shear strength (Su), and compression modulus (Es) parameter fields are realized by trend term separation, DCT sparse reconstruction, and autocorrelation function (ACF) analysis. Results indicate laterally coherent fields with depth-dependent strengthening after detrending and DCT–BCS reconstruction. Inversions of OCR, Su, and Es are consistent with CPTU correlations and capture the differences between the old and new subgrades. The uncertainty analysis of DCT spectrum further shows that the standard deviation (SD) in the low-frequency component is significantly higher than that in the high-frequency component, which verifies the stability of the reconstruction results. The proposed BCS–DCT framework reconstructs spatial fields from sparse, anisotropic CPTU measurements and characterizes their autocorrelation. It complements kriging/GP models by providing ACF-based correlation length diagnostics and posterior uncertainty that aid interpretation. On a representative data set, the ACF inferred by BCS–DCT agrees with that derived from a semivariogram, indicating reliable correlation scales. It provides high-precision and high-efficiency technical support for foundation performance evaluation and differential settlement control in road expansion projects.