Comparative Optimization of Straight vs Curved Retaining Walls in Stiff Sandy Clay and Crushed Pebble Gravel using PLAXIS 3D

Abstract

Based on Optimization of geometry of the deep excavation support system is essential in reducing horizontal displacements, bending moments, and costs of construction. Though previous studies have shown the need for curved retaining walls in expansive soils such as Black Cotton soil, this paper undertakes a 3D finite element parametric study to determine the performance of curved retaining walls which are non-circular against straight retaining walls in moderate to high strength soils. Using PLAXIS 3D software, models were constructed for a 10 meter deep excavation in two different soils that is, Stiff Sandy Clay and Crushed Pebble Gravel. Ultimately, it establishes when an arched geometry serves as an optimal structural choice versus when it becomes economically redundant.

Introduction

This study investigates the performance of curved retaining walls compared with conventional straight retaining walls for deep excavations in stronger soils using PLAXIS 3D finite element analysis. While straight retaining walls rely primarily on bending resistance and require substantial thickness and steel reinforcement for deep excavations, curved retaining walls utilize horizontal arching action to transfer soil pressure along the wall, reducing structural stresses and construction costs. Building on previous work conducted in expansive Black Cotton Soil, this research evaluates whether curved walls continue to offer advantages in Stiff Sandy Clay and Crushed Pebble Gravel, which exert lower lateral earth pressures.

The study reviews previous research showing that curved retaining walls reduce horizontal displacement and bending moments, while three-dimensional numerical analysis provides more accurate predictions than two-dimensional models for complex excavation geometries. Based on these findings, four PLAXIS 3D models were developed to compare straight and curved retaining walls under identical excavation conditions. The numerical models incorporated realistic soil properties, diaphragm walls, capping beams, steel props, staged excavation procedures, and finite element meshing to simulate deep excavation behavior.

Results indicate that curved retaining walls consistently outperform straight walls in both soil types. In Stiff Sandy Clay, the maximum horizontal displacement decreased from 7.0 mm for the straight wall to 5.927 mm for the curved wall, while the maximum bending moment reduced from 79.38 kN·m to 77.40 kN·m. In Crushed Pebble Gravel, the improvements were more significant, with horizontal displacement decreasing from 5.984 mm to 3.305 mm and bending moment reducing from 72.12 kN·m to 71.15 kN·m.

The findings demonstrate that curved retaining walls provide better structural performance by minimizing wall deformation and reducing bending stresses, even in relatively strong soils. Although stronger soils naturally exert lower lateral pressures, the curved geometry still enhances stability through arching action, potentially lowering reinforcement requirements and improving construction efficiency. The study concludes that curved retaining walls remain a practical and cost-effective solution for deep excavations across a range of soil conditions, particularly where minimizing structural movement and stress is critical.

Conclusion

Based on 3D finite element analysis conducted in PLAXIS 3D, the following conclusion are found: 1) Software Models (Mohr-Coulomb vs. Hardening Soil): An important finding from our study is how the wall shape interacts with different soil models in the software. For the Stiff Sandy Clay, the simpler Mohr-Coulomb model worked perfectly, showing a well-controlled wall deflection of 7.00 mm. But for the Crushed Pebble Gravel, we used the more advanced Hardening Soil model. This model proved that the gravel\\\'s massive friction angle 51.80 and interlocking rocks naturally push back against the wall, resulting in an even smaller deflection of just 5.98 mm for a standard straight wall. 2) Superiority of Curved Geometry: After modifying the wall geometry to a non-circular curved or arch drastically improves structural stability and also capitalizes on 3D spatial soil structure interactions. 3) Displacement Reduction: The arched geometry successfully reduced the maximum lateral displacement by 15.3% (from 7mm to 5.927mm) in Stiff Sandy Clay and by 44.76% (from 5.984mm to 3.305mm) in Crushed Pebble Gravel. Additionally, it reduced the maximum horizontal bending moments, actively relieving flexural stress on the concrete panels. 4) Bending Moments: The arched geometry also successfully reduced the Bending Moments by 2.49% (from 79.38 KN-m to 77.40 KN-m) in Stiff Sandy Clay. And 1.34% (from 72.12 KN-m to 71.15 KN-m) in Crushed Pebble Gravel. 5) Economic Optimization: While the curved wall performs exceptionally well, the magnitudes of displacement in these highly competent soils are inherently minimal. Therefore, while the arch serves as an optimal tool for reducing concrete thickness in moderate soils Stiff Sandy Clay, the added construction complexity of an arched wall may be economically redundant in extremely high-friction environments like Crushed Pebble Gravel.

References

[1] Sandip M Chavan, Dr. Vijay Sharma, “Behaviour of Retaining Wall in Black Cotton Soil”, International Research Journal of Engineering and Technology (IRJET), Volume: 04 Issue: 07, July 2017, Pp: 780-784. [2] Jakub Stacho, Monika Sulovska (2019). \\\"Numerical Analysis of Soil Improvement for a Foundation of a Factory Using Stone Columns Made of Different Types of Coarse-grained Materials,\\\" Periodica Polytechnica Civil Engineering, 63(3), 795–803. [3] Daniel Gilmore, Raul Fuentes, “Predicting the behaviour of non-circular, curved-in-plan retaining walls using the trial load method”, 19th International Conference on Soil Mechanics and Geotechnical Engineering, Seoul, 2017, Pp: 1987-1990. [4] Zhang, Y. P., & Zhang, T. Q., Behaviour Analysis of Cantilever Arched Retaining Structures in Foundation Pits,\\\" Journal of Zhejiang University (SCIENCE), Volume: 2, No. 3, Pp: 309-312. [5] H. F. Schweiger, F. Scharinger, & R. Lüftenegger, “3D finite element analysis of a deep excavation and comparison with in situ measurements” Geotechnical Aspects of Underground Construction in Soft Ground, Taylor & Francis Group, Pp: 193-199. [6] Plaxis 3D Connect Edition V20 | Tutorial Manual [7] Table 2: The Properties used for Stiff sandy clay & Crushed pebble gravel, Source: Plaxis 3D Tutorial, Pp:71, Source: Jakub Stacho, Monika Sulovska (2019). \\\"Numerical Analysis of Soil Improvement for a Foundation of a Factory Using Stone Columns Made of Different Types of Coarse-grained Materials,\\\" Pp:798 [8] Table 3: Dimensions of the wall, Source: Daniel Gilmore, Raul Fuentes, “Predicting the behaviour of non-circular, curved-in-plan retaining walls using the trial load method”, Pp: 1989 [9] Table 5,6: The Properties used for Diaphragm Wall, Capping Beam, Source: BS EN 1991-1-1:2002, The Concrete Society, [No date], Goh, 1993 and Richards and Powrie, 1994. [10] Table 7: The Properties used for Steel Prop, Source: EN 1993-1-1:2005, Geocentrix, 2004.

Copyright

Copyright © 2026 Aditya Raghuwanshi, Dr. Raghvendra Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.