Analytical Expression for Plastic Hinge Length in Extended Pile-shafts

"Equivalent fixed-base cantilever model is a common approach for performance base seismic design of bridge structures supported by extended pile-shaft. In this method, global displacement ductility factor is related to local curvature ductility demand by assuming a concentrated plastic hinge at location of maximum bending moment. Equivalent plastic hinge length is one of the key parameters that should be assumed accurately in kinematic expression of the cantilever model. Although, some expressions have proposed to estimate the length of the in-ground plastic hinge; however, these relations yield differing results. In this paper, a general expression is derived based on the concept of distributed plasticity to predict the plastic region of yielded piles in clay and sand. A length modification factor is defined to relate the equivalent length of plastic hinge to the real plastic zone. Then, results from nonlinear pushover analyses are used to propose an equation for the modification factor as a function of displacement ductility factor.IntroductionDuring severe earthquake events, development of the plastic hinge in pile foundation below ground level is inevitable for bridge structures supported on extended pile-shafts. A common approach for seismic design of the yielding pile-shafts is to replace the pile-soil system by an equivalent fixed-base cantilever assuming the equivalent system has the same global response as that of the pile-shaft (Budek et al. 2000; Chai 2002). In this method, plastic curvature is concentrated at the center of the equivalent plastic hinge below ground surface. Prior knowledge of plastic-hinge length is essential for proper assessment of assess plastic displacement at the top of the pile-shaft. Unfortunately, existing recommendations for estimating plastichinge length are largely incomplete and/or inadequate.During the last two decades, several relationships have proposed for evaluating the equivalent plastic hinge length, Lp, based on experimental and numerical studies. Budek et al. (2000) conducted numerical modeling to calculate the plastic-hinge length of piles embedded in cohesionless soil. They found that the plastichinge length varies linearly with both soil stiffness and aboveground height, e. Chai and Hutchinson (2002) conducted full-scale experimental tests on reinforced concrete piles in sand. They reported that Lp depends primarily on the aboveground height of the pile, neither sensitive to the soil stiffness nor to the value of displacement ductility factor. They stated that the equivalent plastic hinge length is relatively independent of the displacement ductility factor and is not very sensitive to the change in soil density. On the contrary, Goel (2014) and Liu et al. (2016) conducted nonlinear numerical analyses which revealed that Lp changes with the displacement ductility factor and even suggested that using different values of Lp for different seismic design levels is essential for a reliable estimation of the ductility capacity."