A hardening soil-spring model with small-strain stiffness for confined excavations and its application
LU Dechun1, 2, HUANG Ming3, LAI Fengwen3*, ZHOU Xin1, DU Xiuli2
(1. School of Architecture and Civil Engineering, Xiamen University, Xiamen, Fujian 361005, China; 2. Institute of Geotechnical and Underground Engineering, Beijing University of Technology, Beijing 100124, China; 3. School of Civil Engineering, Fuzhou University, Fuzhou, Fujian 350116, China)
Abstract：Elastic beam-spring models are widely used in performance-based design for confined excavations; however, existing methodologies are often insufficient in accurately capturing the evolution of earth pressures under confined spatial constraints and the nonlinear stiffness behavior of soil. To address these limitations, this study develops a hardening soil-spring model with small-strain stiffness within a nonlinear elastic beam-spring framework to predict deformations in confined excavations. The proposed model features a displacement-dependent earth pressure formulation with a modified factor applied to the active side of the retaining structure, effectively accounting for soil arching effects and horizontal shear stresses within the confined soil. On the passive side, nonlinear soil springs simulate both the hardening behavior and small-strain characteristics of soil based on the hardening soil model with small-strain stiffness (HSS). The proposed model is validated against centrifuge test results and numerical simulations, followed by a parametric analysis that examines the effects of excavation depth, confined soil width, wall bending stiffness, and soil stiffness parameters—including Young?s modulus and small-strain stiffness—on wall deflections. Additionally, the model is applied to a real-world case involving deep excavations adjacent to bridge piers in a coastal composite stratum, with soil parameters derived from in-situ standard penetration tests (SPT) and cross-hole seismic tests. The close agreement between predictions and field monitoring results highlights the practical applicability of the proposed model.
路德春1，2，黄 明3，赖丰文3*，周 鑫1，杜修力2. 受限空间基坑小应变硬化土弹簧模型及其应用[J]. 岩石力学与工程学报, 2026, 45(7): 2201-2213.
LU Dechun1, 2, HUANG Ming3, LAI Fengwen3*, ZHOU Xin1, DU Xiuli2. A hardening soil-spring model with small-strain stiffness for confined excavations and its application. , 2026, 45(7): 2201-2213.
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2026, Vol. 45 
