<p>The hardening soil small-strain (HSS) model is widely recognized for its ability to simulate complex soil stress paths, leading to improved prediction accuracy in geotechnical engineering. However, its practical application is often hindered by the large number of required parameters and their significant regional variability, making determination costly and time-consuming. To address this, we propose a machine learning-based framework for efficient determination of locality-specific HSS parameters. The method begins with a statistical analysis of parameter ratios relative to the compression modulus <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\text{E}}_{{\text{s}}}^{{1 {-} 2}}\)</EquationSource> </InlineEquation> to identify sensitive and non-sensitive parameters. For sensitive parameters with high regional variability, a parameter sampling design is implemented within established value ranges. A BP neural network is then trained to establish a nonlinear mapping between parameter combinations and foundation pit displacements, enabling intelligent inverse analysis. The proposed method is applied to typical strata in Qingdao, China—plain fill, silty clay, and medium-fine sand—where regional HSS parameters were previously unavailable. Through validation with two independent cases, numerical simulations using inversion parameters showed a high consistency with on-site monitoring data: the root mean square error (RMSE) for both the lateral displacement of the retaining structure and ground settlement was below 0.51 mm, and the mean absolute error was below 0.4 mm. The key inversion parameter ratios for the Qingdao region have been determined as follows: the results show that the values of HSS parameters in Qingdao obtained by machine learning are as follows: <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\text{G}}_{{0}}^{{{\text{ref}}}}\)</EquationSource> </InlineEquation>:<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\text{E}}_{{{\text{ur}}}}^{{{\text{ref}}}}\)</EquationSource> </InlineEquation>:<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({\text{E}}_{{{50}}}^{{{\text{ref}}}}\)</EquationSource> </InlineEquation>:<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({\text{E}}_{{{\text{oed}}}}^{{{\text{ref}}}}\)</EquationSource> </InlineEquation>:<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\({\text{E}}_{{\text{s}}}^{{1 {-} 2}}\)</EquationSource> </InlineEquation> can be taken as 5.24:4.64:1:1:1 for plain fill; 14.74:6.00:1:1:1 for silty clay; and 11.50:5.02:1:1:1 for medium-fine sand.</p>

Machine learning-based method for determining regional parameters of the HSS model: a case study of Qingdao, China

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2026年3月11日

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Changfeng Yuan,
Qiming Zhang,
Hao Feng,
Ke Wang,
Shunzhe Zhang

摘要

The hardening soil small-strain (HSS) model is widely recognized for its ability to simulate complex soil stress paths, leading to improved prediction accuracy in geotechnical engineering. However, its practical application is often hindered by the large number of required parameters and their significant regional variability, making determination costly and time-consuming. To address this, we propose a machine learning-based framework for efficient determination of locality-specific HSS parameters. The method begins with a statistical analysis of parameter ratios relative to the compression modulus \({\text{E}}_{{\text{s}}}^{{1 {-} 2}}\) to identify sensitive and non-sensitive parameters. For sensitive parameters with high regional variability, a parameter sampling design is implemented within established value ranges. A BP neural network is then trained to establish a nonlinear mapping between parameter combinations and foundation pit displacements, enabling intelligent inverse analysis. The proposed method is applied to typical strata in Qingdao, China—plain fill, silty clay, and medium-fine sand—where regional HSS parameters were previously unavailable. Through validation with two independent cases, numerical simulations using inversion parameters showed a high consistency with on-site monitoring data: the root mean square error (RMSE) for both the lateral displacement of the retaining structure and ground settlement was below 0.51 mm, and the mean absolute error was below 0.4 mm. The key inversion parameter ratios for the Qingdao region have been determined as follows: the results show that the values of HSS parameters in Qingdao obtained by machine learning are as follows: \({\text{G}}_{{0}}^{{{\text{ref}}}}\) : \({\text{E}}_{{{\text{ur}}}}^{{{\text{ref}}}}\) : \({\text{E}}_{{{50}}}^{{{\text{ref}}}}\) : \({\text{E}}_{{{\text{oed}}}}^{{{\text{ref}}}}\) : \({\text{E}}_{{\text{s}}}^{{1 {-} 2}}\) can be taken as 5.24:4.64:1:1:1 for plain fill; 14.74:6.00:1:1:1 for silty clay; and 11.50:5.02:1:1:1 for medium-fine sand.