Amirkabir University of Technology Amirkabir Journal of Civil Engineering 2588-297X 57 12 2026 02 20 Hybrid Boundary-Finite Element Method for Modeling Artificial Freezing in Soil Environment Including Rock Type Inhomogeneities Hybrid Boundary-Finite Element Method for Modeling Artificial Freezing in Soil Environment Including Rock Type Inhomogeneities 2033 2054 6006 10.22060/ceej.2026.24756.8345 FA Bahman Ansari Department of Civil Engineering, Faculty of Engineering, University of Zanjan, Zanjan Alireza Firoozfar Department of Civil Engineering, Faculty of Engineering, University of Zanjan, Zanjan,, Iran Journal Article 2025 09 18 This research proposes a hybrid numerical method, for modeling the development of artificial ground freezing in soil containing subsurface inhomogeneities. In this approach, by combining the Boundary Element Method (BEM) and employing time-independent fundamental solutions, appropriate boundary integral equations are developed. The volume integrals arising from the presence of dynamic terms are incorporated into the equations using the Finite Element Method (FEM). For this purpose, a type of boundary-finite element, combining a quadratic boundary element with a three-node triangular finite element, was developed, and the solvable forms of the final equations were presented. <br /><br />Subsequently, by implementing the hybrid method into a computational algorithm, its accuracy and efficiency was evaluated and validated by solving several benchmark examples. Finally, in a parametric study, the application of the hybrid method for modeling the development of artificial freezing in saturated soil containing a inhomogeneities in the form of an unsaturated rock mass is described. The effects of varying the cross-sectional area of the inhomogeneities and its distance from the freeze pipe were evaluated. <br /><br />The results of the parametric study indicate that the presence of the inhomogeneities reduces the volume of the freeze bulb by up to 20%. Furthermore, inhomogeneities with a circular cross-section were more limited the development of freezing compared to a square shape. This research proposes a hybrid numerical method, for modeling the development of artificial ground freezing in soil containing subsurface inhomogeneities. In this approach, by combining the Boundary Element Method (BEM) and employing time-independent fundamental solutions, appropriate boundary integral equations are developed. The volume integrals arising from the presence of dynamic terms are incorporated into the equations using the Finite Element Method (FEM). For this purpose, a type of boundary-finite element, combining a quadratic boundary element with a three-node triangular finite element, was developed, and the solvable forms of the final equations were presented. <br /><br />Subsequently, by implementing the hybrid method into a computational algorithm, its accuracy and efficiency was evaluated and validated by solving several benchmark examples. Finally, in a parametric study, the application of the hybrid method for modeling the development of artificial freezing in saturated soil containing a inhomogeneities in the form of an unsaturated rock mass is described. The effects of varying the cross-sectional area of the inhomogeneities and its distance from the freeze pipe were evaluated. <br /><br />The results of the parametric study indicate that the presence of the inhomogeneities reduces the volume of the freeze bulb by up to 20%. Furthermore, inhomogeneities with a circular cross-section were more limited the development of freezing compared to a square shape. https://ceej.aut.ac.ir/article_6006_91ba4a4478a66bee9812b0804b6f9d1b.pdf