Citation: Eilat, T.; Mitelman, A.; McQuillan, A.; Elmo, D. A Comparative Study of Embedded Wall Displacements Using Small-Strain Hardening Soil Model. Geotechnics 2024, 4, 309–321. https://doi.org/10.3390/ geotechnics4010016 Received: 17 February 2024 Revised: 1 March 2024 Accepted: 4 March 2024 Published: 8 March 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Article A Comparative Study of Embedded Wall Displacements Using Small-Strain Hardening Soil Model Tzuri Eilat 1 , Amichai Mitelman 1 , Alison McQuillan 2 and Davide Elmo 3, * 1 Department of Civil Engineering, Ariel University, Ariel 4077625, Israel; tzuri.eilat@msmail.ariel.ac.il (T.E.); amichaim@ariel.ac.il (A.M.) 2 Rocscience Inc., Toronto, ON M5T 1V1, Canada; alison.mcquillan@rocscience.com 3 Department of Mining Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada * Correspondence: delmo@mining.ubc.ca Abstract: Traditional analysis of embedded earth-retaining walls relies on simplistic lateral earth pressure theory methods, which do not allow for direct computation of wall displacements. Contem- porary numerical models rely on the Mohr–Coulomb model, which generally falls short of accurate wall displacement prediction. The advanced constitutive small-strain hardening soil model (SS-HSM), effectively captures complex nonlinear soil behavior. However, its application is currently limited, as SS-HSM requires multiple input parameters, rendering numerical modeling a challenging and time- consuming task. This study presents an extensive numerical investigation, where wall displacements from numerical models are compared to empirical findings from a large and reliable database. A novel automated computational scheme is created for model generation and advanced data analysis is undertaken for this objective. The main findings indicate that the SS-HSM can provide realistic predictions of wall displacements. Ultimately, a range of input parameters for the utilization of SS-HSM in earth-retaining wall analysis is established, providing a good starting point for engineers and researchers seeking to model more complex scenarios of embedded walls with the SS-HSM. Keywords: embedded walls; earth-retaining walls; hardening soil model; geotechnical analysis; numerical modeling; machine learning 1. Introduction Embedded retaining walls are ubiquitous structures installed prior to excavation and designed to support the lateral pressures due to different ground levels on each side of the wall. The stability of embedded walls relies on the penetration beneath the level of the lower side. These walls are used for a wide range of construction projects, including basements, cut-and-cover tunnels, landscaping, and underground infrastructure installation. Types of walls include pile walls, sheet pile walls, diaphragm walls, and more. For shallow excavations, cantilever walls are sufficient. For deep excavations, lateral supports, such as struts or ground anchors, are installed according to a staged excavation plan. The increase in urbanized areas is pressuring the geotechnical community, which is currently challenged by a demand to better predict wall behaviour and displacement [1]. In turn, advancing geotechnical analysis methods is crucial for obtaining safe and economic structural design [2]. The design methods for these walls are varied, while traditional analysis largely relies on limit equilibrium approaches, according to earth lateral pressure theory [3]. Under this approach, active and passive pressures are imposed on the wall according to the assumed wall movements, and the resultant internal forces and bending of the wall are computed. An excellent review of the embedded cantilever wall problem is given by [4]. The process of computing the embedment depth and internal forces in the wall is described in detail. Figure 1 shows typical problem geometry and the active and passive lateral pressures for the cantilever problem. Accordingly, H is the excavation depth, O is the point of wall Geotechnics 2024, 4, 309–321. https://doi.org/10.3390/geotechnics4010016 https://www.mdpi.com/journal/geotechnics