Prediction of the nonlinear pull-out response of FRP ground anchors using an analytical transfer matrix method

Fiber-reinforced polymer (FRP) rods have been increasingly used in grouted ground anchors due to their high strength-to-weight ratio, excellent corrosion resistance, and convenience in incorporating the fiber sensing technology. To establish their pull-out capacity, FRP rods are usually embedded within a grouted steel tube and then subjected to pull-out in the laboratory. The aim of this paper is to develop a numerical method for predicting the nonlinear pull-out response of FRP rods embedded in steel tubes filled with cement grout. In the method, the cement grout is assumed to be subject to simple shear, the local interfacial bond stress-slip model of the bar-to-grout interface is represented by a piece-wise curve comprising elastic, softening, and frictional stages, and the unloading effect is also taken into account. A set of two second-order ordinary differential equations are derived in terms of the displacements of the FRP rod and steel tube and solved analytically to formulate the element transfer matrix. When the thickness of the steel tube approaches infinity, this method can be applied to the problem of FRP rods embedded in rock. Based on the developed numerical method, the interfacial bond properties and snapback phenomenon are analyzed. After the method is validated by comparisons with four sets of experimental data, the effects of the radius and length of FRP rods, the local peak bond stress and the residual frictional strength on the maximum pull-out load are evaluated in a quantitative manner.