School of Civil and Environmental Engineering

Ph.D. Thesis Defense Announcement

Interval Finite Element Approach for Stability Analysis of Concrete Gravity Dams under Uncertainties

By Binod Yadav

Advisor:

Dr. Rafi L. Muhanna

Committee Members:

Dr. Abdul-Hamid Zureick (CEE)

Dr. Haiying Huang (CEE)

Dr. George Kardomateas (Aerospace Engineering)

Dr. Bal K. Khadka (GMC, Dept. of Mathematics)

Date and Time: November 5, 2025. 3 PM – 5 PM EST

Location: Sustainable Education Building (SEB) # 122

Teams Meeting ID: 262 203 862 185 1

Passcode: JH9Y9HL2

ABSTRACT
The stability of concrete gravity dams is a critical safety concern, particularly under the influence of uncertain loading and strength parameters. In current engineering practice, the crack-based Limit Equilibrium Method (LEM) relies on simplified assumptions and frequently yields conservative results with excess safety margins. In particular, LEM relies on the linear Mohr–Coulomb (MC) shear strength envelope and crack initiation criteria based only on the location of the resultant force. While the Mohr–Coulomb (MC) shear strength model is suitable for foundation where no asperities exist, most concrete gravity dams are founded on rock foundation, where asperities are present along
the concrete–foundation rock interface. Due to these asperities, the Mohr–Coulomb (MC) model underestimates the shear strength of the sliding interface. Probabilistic methods, such as Monte Carlo Simulation (MCS), provide valuable insight but require extensive site-specific data and probability distributions that are rarely available for existing dams.
This research develops a novel Interval Finite Element Method (IFEM) framework to overcome these limitations by explicitly incorporating uncertainties in dam stability analysis, utilizing the nonlinear Barton–Choubey (BC) shear strength model, which accounts for the presence of asperities along the dam foundation. All sources of uncertainty are expressed in interval form and incorporated within the IFEM framework to evaluate the structural response of concrete gravity dams under parameter uncertainty. The proposed framework integrates interval arithmetic with the nonlinear Barton–Choubey shear strength model, an element-by-element assembly strategy to reduce dependency effects, and a new crack initiation and propagation criterion based on both tensile and shear stresses that iteratively updates uplift pressure and boundary conditions as the crack propagates. Together, these innovations enable realistic modeling of crack–uplift interaction and provide mathematically guaranteed enclosures of structural response.
The methodology was validated through a concrete gravity dam case study, where uncertain parameters, including Young’s modulus, concrete density, water unit weight, joint roughness coefficient (JRC), joint wall compressive strength (JCS), and residual friction angle, were expressed in interval form using laboratory test data, historical NOAA temperature records, and construction photographs. Results demonstrated that the dam remains stable, with interval factors of safety above unity and crack lengths consistent with MCS predictions, while avoiding the excessive safety margins associated with LEM.
By providing reliable, computationally feasible, and data-efficient safety bounds, the proposed IFEM framework offers dam owners and regulators a powerful tool for evaluating stability under uncertainty. This approach not only improves confidence in safety assessments but also has the potential to reduce unnecessary remediation measures, leading to safer and more cost-effective management of aging dam infrastructure.