Shutong Yang

Analytical Solution for Fracture Analysis of CFRP Sheet–Strengthened Cracked Concrete Beams

Fiber-reinforced polymer (FRP) composite materials have been widely used in the field of retrofitting. Theoretical analysis of FRP plate- or sheet-strengthened cracked concrete beams is necessary for estimating service reliability of the structural members. In previous studies, the effect of a perfectly bonded FRP plate or sheet was equivalent to a cohesive force acting at the bottom of crack to delay the crack propagation in concrete and reduce the crack width. However, delamination between FRP and cracked beam is inevitable due to interfacial shear stress concentration at the bottom of crack. The intention of this paper is to present an analytical solution for fracture analysis of carbon FRP (CFRP) sheet–strengthened cracked concrete beams by considering both vertical crack propagation in concrete and interfacial debonding at CFRP-concrete interface. The interfacial debonding is modeled as the interfacial shear crack propagation in this paper. Four different stages are discussed after initial cracking state of the concrete. At the first stage, only fictitious crack propagation occurs in the concrete. At the second stage, macrocrack propagates in the concrete without interfacial debonding. At the third stage, both vertical macrocrack propagation in the concrete and horizontal shear crack propagation at the CFRP-concrete interface occur in the strengthened beam. The tensile stress in the CFRP sheet and interfacial shear stress along the span are formulated based on the deformation compatibility condition at the CFRP-concrete interface at this stage. Finally, macroshear crack propagates at the interface until the CFRP sheet is completely peeled out from the beam, and then the member is fractured. The applied load is determined as a function of the referred two crack lengths at different stages. At the beginning, the applied load increases to one peak value with the full propagation of fictitious crack at the first stage. At the third stage, the applied load is improved to another peak value due to the relatively high cohesive effect of the CFRP sheet. Then the two peak values are determined by the Lagrange multiplier method. The validity of the proposed analytical solution is verified with the experimental results and numerical simulations. It can be concluded that the proposed analytical solution can predict the load-bearing capacity of CFRP sheet-strengthened cracked concrete beams with reasonable accuracy.

Correlation between cohesive crack-tip local fracture energy and peak load in mortar beams

Mortar, as concrete-like coarse-structured materials, has a fracture process zone ahead of crack tip after the crack initiation. The maximum fracture load must be related to the cohesive crack-tip local fracture energy due to the relatively limited crack growth in the critical state. The intention of this paper is to correlate the local fracture energy with the maximum loads in mortar specimens. An analytical approach is proposed on the correlation between the two parameters. Then a fracture test has been performed on three-point-bending notched mortar beams with a wide range of notch depths. Upon comparison of the predicted and experimentally measured peak loads, it is found that the crack-tip local fracture energy indeed varies with notch depth and beam height. Thus, the trilinear model for the local fracture energy distribution is confirmed in mortar specimens, indicating both the front and back free boundary effects. Based on the trilinear model, the size-independent fracture energy can be obtained if the notch depth and the ligament length are long enough. The proposed approach is analytical and convenient without the load-displacement curves in tests.

An Analytical Model to Predict the Push-Out Capacity of Mortar from Rock Block

Ground anchors have been very practical in a wide range of geotechnical structures. Good bond properties at the anchor-mortar and mortar-rock interfaces can ensure transmitting an applied tensile load to a load bearing structure efficiently. The bond performance between the mortar and rock is necessary to be studied. A push-out test of mortar from rock block can be used to analyze the interfacial properties between the two materials. In this paper, an analytical model is proposed to determine the push-out capacity of mortar from rock block. Based on the deformation compatibility at the interface, the compressive stress in the mortar and the interfacial shear stress at the mortar-rock interface are formulated at different loading stages. By modeling interfacial debonding as an interfacial shear crack, the push-out load is then expressed as a function of the interfacial crack length. In virtue of the Lagrange Multiplier Method, the maximum push-out load is determined. The validity of the proposed model is verified with the experimental results. It can be concluded that if the interfacial parameters at the mortar-rock interface are obtained, the push-out capacity of mortar from rock block can be accurately determined using the proposed model. The proposed solution in this paper would provide a good theoretical basis in evaluating the stability of ground anchors in practice.