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Geomechanics and Engineering Volume 43, Number 5, December10 2025 , pages 369-378 DOI: https://doi.org/10.12989/gae.2025.43.5.369 |
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Reliability-based optimization of MSE walls considering internal stability |
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Zafar Mahmood, Mohsin Usman Qureshi, Ali Murtaza Rasool and Syed Bilal Ahmed Zaidi
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| Abstract | ||
| This study presents a reliability-based optimization (RBO) framework for the internal stability of mechanically stabilized earth walls, addressing reinforcement rupture and pullout limit states. The target reliability is set to B = 3.09 (Pf = 10−3). The MSE wall, reinforced with steel strips, founded on cohesionless soil, with horizontal backfill and uniform live traffic surcharge is considered. Uncertain variables in rupture and pullout limit states are unit weight and friction angle of backfill soil; uniform live surcharge load; and yield strength of steel strips. The reliability index is calculated by the first-order reliability method (FORM). Constrained optimization with linear approximation (COBYLA) is used for determination of reliability index and optimization of reinforcement length. For rupture, optimizing horizontal spacing at fixed vertical spacing yields designs that satisfy B > 3.09 at every depth with minimum factor of safety FSRP = 1.7 to 1.8 and a near heightindependent B–FS relationship. For pullout, optimizing strip length shows the required length-to-height ratio decreases with wall height and tighter vertical spacing: representative maxima of L/Hare 1.27, 0.83, 0.5 for H = 10 m at vertical spacing Sv = 1, 0.75, 0.5 m; 1.01, 0.7, 0.48 for H = 15 m; and 0.83, 0.6, 0.43 for H = 20 , respectively. Across cases, designs meeting B = 3.09 deliver factor of safety FS PG =2.10 at critical depth, but no unique B–FS mapping emerges for pullout. The framework converges to B-compliant, materially efficient layouts and clarifies how wall height and reinforcement spacing jointly control optimal L/H for pullout while leaving rupture behavior chiefly governed by spacing rather than wall height. | ||
| Key Words | ||
| constrained optimization; first-order reliability method; internal stability; MSE wall; reliability-based optimization | ||
| Address | ||
| Zafar Mahmood: Department of Civil Engineering, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia Mohsin Usman Qureshi: Faculty of Engineering, Sohar University, Sohar, Oman Ali Murtaza Rasool: National Engineering Services Pakistan, Lahore, Pakistan Syed Bilal Ahmed Zaidi: University of Engineering and Technology Taxila, Taxila, Pakistan | ||