Abstract This paper proposes a general formulation for physics-based probabilistic models that are computationally convenient for uncertainty quantification and reliability analysis of complex systems while integrating the governing physical laws. The proposed formulation starts with the prediction of the quantities of interest using differential equations that represent the governing physical laws. For computational efficiency, the solution of the governing differential equations might be approximated. The predictions from the differential equations are then improved by introducing analytical correction terms that capture those physical characteristics of the phenomenon not fully captured by the differential equations. The paper also presents nested probabilistic models for uncertain physical characteristics that are difficult to measure. Observational data are required to calibrate the nested probabilistic models and correction terms. To provide context, the paper discusses physics-based probabilistic models for a class of boundary value problems that includes as a special case, the steady advection–diffusion–reaction equation, governing a diverse range of physical, chemical, and biological phenomena. Using the Bayesian approach, the differential equations are combined with observational data and any prior information to estimate the unknown model parameters and uncertain system characteristics. The paper then formulates the reliability problem for the computation of failure probability of physical and engineering systems using the proposed physics-based probabilistic models. To illustrate, the paper considers the reliability analysis of axially loaded rock socketed drilled shafts.

#1Pouyan Asem(UMN: University of Minnesota)H-Index: 6

#2Paolo Gardoni(UIUC: University of Illinois at Urbana–Champaign)H-Index: 48

Abstract The design of socketed foundations in weak sedimentary rocks is often governed by settlement. The shear stiffness of the rock socket sidewalls, and the normal stiffness of the rock socket base are the main parameters that affect the settlement of rock sockets at service load conditions and are needed for settlement calculation in load-transfer method or using the theory of elasticity. In this paper, in situ load test data for socketed foundations in weak rocks are collected. The shear s...

#1Pouyan Asem(UMN: University of Minnesota)H-Index: 6

Abstract This paper presents a probabilistic limit state framework for the evaluation of the base resistance of drilled shafts in soft rock. In situ load tests and the Griffith fracture theory are used to evaluate the mode of failure for the rock mass under the drilled shaft base. The base resistance or the limit state in the context of this paper is defined by the contact pressure at which load induced vertical to subvertical cracks form and the contact pressure-displacement relationship passes...

#1Pouyan Asem(UMN: University of Minnesota)H-Index: 6

#2Paolo Gardoni(UMN: University of Minnesota)H-Index: 48

Abstract The shear stress and shear displacement relationship for the rock socket sidewalls is required for the calculation of the drilled shaft butt settlement under the service loads. This paper first introduces a comprehensive database of in situ axial load tests on drilled shafts, anchors and plugs that are embedded in different soft rock formations. The database includes measurements of (i) the initial shear stiffness, (ii) the peak shear stress and (iii) the post-peak reduction in shear st...

#1Pouyan Asem(UIUC: University of Illinois at Urbana–Champaign)H-Index: 6

#2Vashish Taukoor(UIUC: University of Illinois at Urbana–Champaign)H-Index: 2

Last. Thierno Kane(UIUC: University of Illinois at Urbana–Champaign)H-Index: 3

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Abstract The average degree of consolidation of soft rock mass in the immediate vicinity of the base of drilled shaft or plate load tests was evaluated using the Biot Three-Dimensional Consolidation Theory. The compressibility parameters of soft rock mass were estimated using the contact pressure and displacement relationships obtained from the in situ drilled shaft and plate load tests. It was found that typical drilled shaft and plate load tests on soft rocks are drained to partially drained, ...

#1Bo Sun(Zhejiang University of Technology)H-Index: 2

#2Paolo Gardoni(UIUC: University of Illinois at Urbana–Champaign)H-Index: 48

A comprehensive directional search algorithm is developed for the model development and selection of hierarchical models systems. A hierarchical model system is a system of nested single-level models that includes different model candidates that can be constructed and calibrated independently. Adjusted single-level model candidates for hierarchical (multi-level) model selection are constructed following the general process of probabilistic single-level model development and selection. An uncerta...

#2Paolo Gardoni(UIUC: University of Illinois at Urbana–Champaign)H-Index: 48

Last. Mauro Sassu(University of Cagliari)H-Index: 16

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Probabilistic models for the concentrated leak erosion of earthen water retaining structures are presented. The models predict the values of the critical shear stress, the coefficient of erosion and the pipe radius enlargement, starting from other measurable soil properties and the geometrical dimensions of the embankment. The models account for both the non-cohesive and cohesive contributions to the erosion behavior. A Bayesian approach is used for the treatment of the unknown parameters. An im...

#1Gaofeng Jia(CSU: Colorado State University)H-Index: 12

#2Paolo Gardoni(UIUC: University of Illinois at Urbana–Champaign)H-Index: 48

Abstract For performance analysis of deteriorating engineering systems, it is critical to model and incorporate the various deterioration processes and associated uncertainties. This paper proposes state-dependent stochastic models (SDSMs) for modeling the impact of deterioration on the performance of engineering systems. Within the stochastic framework, the change of the system state variables due to different deterioration processes and their interaction is modeled explicitly. As a candidate m...

#1Neetesh Sharma(UIUC: University of Illinois at Urbana–Champaign)H-Index: 3

#2Armin Tabandeh(UIUC: University of Illinois at Urbana–Champaign)H-Index: 8

Last. Paolo Gardoni(UIUC: University of Illinois at Urbana–Champaign)H-Index: 48

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AbstractThe resilience of a system is related to its ability to withstand stressors, adapt, and rapidly recover from disruptions. Two significant challenges of resilience analysis are to (1) quantify the resilience associated with a given recovery curve; and (2) develop a rigorous mathematical model of the recovery process. To quantify resilience, a mathematical approach is proposed that systematically describes the recovery curve in terms of partial descriptors, called resilience metrics. The p...

#1Pouyan Asem(UMN: University of Minnesota)H-Index: 6

#2Paolo Gardoni(UIUC: University of Illinois at Urbana–Champaign)H-Index: 48

Abstract Rock mass elastic and strength properties are needed for calculation of deformation and determination of stability of underground structures. Most available models for prediction of rock mass properties are site-specific, are deterministic, and cannot properly propagate uncertainty in reliability analysis of underground structures. A generalized Bayesian approach is used to develop probabilistic predictive models for the rock mass properties. A set of training and testing databases for ...

Last. Mauro Sassu(University of Cagliari)H-Index: 16

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AbstractUnreinforced masonry (URM) buildings make up a significant portion of the built environment, with hollow clay being the predominant choice for the units. The capacity of URM buildings is a ...

#1Pouyan Asem(UMN: University of Minnesota)H-Index: 6

#2Paolo Gardoni(UIUC: University of Illinois at Urbana–Champaign)H-Index: 48

Sockets are often constructed into weak rock mass to improve their axial response to applied compressive or tensile loads. This paper first establishes two separate load test databases for the side and base resistances in in situ socket load tests in weak rocks. The databases include the rock socket geometry, rock socket load–displacement response and the rock mass properties. The paper then reviews the available models for the prediction of (i) the axial resistance (compression or uplift), and ...