Fracture Mechanics Based Residual Strength Assessment of Concrete Members under Fatigue Loading

Abstract

Although concrete is one of the most widely used building materials in the world, there are gaps in our understanding of its behavior under fatigue loading conditions. Structures are subjected to numerous load applications during their service lives, often involving stress reversals, and concrete is known to deteriorate in both strength and stiffness under such repeated loading.

In this study, analytical models are developed for plain and reinforced concrete members to predict residual strength during service life.

Phase I - Plain Concrete Beams Residual strength of plain concrete beams under fatigue loading is assessed.

A linear-elastic fracture mechanics-based fatigue law is proposed to predict crack propagation rate.

The law incorporates effects of external loading frequency and variable amplitude loading.

The quasi-brittle nature of concrete is considered by including tension-softening response in the fracture process zone.

A two-step approach is followed:

Determining the effective critical crack length for unstable fracture using crack extension resistance.

Estimating residual capacity as a function of crack length.

Moment-carrying capacity is obtained as a function of increasing crack length, incorporating tension softening.

Phase II - Fracture and Damage Mechanics A correlation between fracture mechanics and damage mechanics is developed using energy equivalence concepts.

Strength and stiffness reduction due to progressive cracking are characterized using reduction indices.

Numerical examples show good agreement between fracture and damage mechanics indices.

A discrete crack can be modeled as an equivalent damage zone, both corresponding to the same energy loss.

Critical fracture properties such as fracture energy can be obtained by knowing the critical damage zone dimension.

Finite Element Modeling Progressive cracking is modeled using crack beam elements, accounting for compliance variation due to discrete cracking.

Global stiffness degradation is computed using a new damage index based on the minimum eigenvalue of the global stiffness matrix.

An analytical methodology relates local damage parameters (e.g., crack length, CTOD/CMOD) with the global damage index.

The global index is then used to predict residual strength and stiffness of the member.

The procedure is extended to reinforced concrete members for predicting residual fatigue strength.

Probabilistic Study A probabilistic analysis is performed to determine sensitivity of parameters in the fatigue process.

Reliability of a fatigue component is most sensitive to loading frequency, followed by maximum amplitude and initial notch length.