Trilinear Bond-slip Model Research Articles

Effects of Shear Characteristics of Anchoring Interface on Bearing Performance of Fully Grouted Bolts Based on Variable Controlling Method

The shear strength parameter of an anchoring interface is one of the key parameters affecting the design of bolt support. To better realize the design of bolt support, the pullout model of fully grouted bolts was established by FLAC3D numerical software. The commonly used tri-linear bond-slip model of the anchoring interface was selected. The variable controlling method was used to investigate the effects of the shear strength parameters of the anchoring interface on the bearing performance of fully grouted bolts. The results show that, with the increase in the displacement at the peak shear stress, the bearing capacity and the energy absorption of fully grouted bolts decrease and the ability of the fully grouted anchoring system to resist external loads weakens. Meanwhile, the deformation capacity of fully grouted bolts increases, and the durability of the fully grouted anchoring system is enhanced. With the increase in the residual shear stress and the displacement at the residual shear stress, the bearing capacity and deformation capacity of fully grouted bolts both increase, and the energy absorption also increases. Increasing the post-peak bearing properties of the anchoring interface can help improve the bearing performance of fully grouted bolts and enhance the ability of the fully grouted bolts to resist failure. The results may provide guidance for support design and performance enhancement of fully grouted bolts.

Pullout behavior of recycled macro fibers in the cementitious matrix: Analytical model and experimental validation

A novel mechanical recycling method has been recently developed in the authors’ group for processing waste glass fiber-reinforced polymer (GFRP) composites into macro fibers, which are then incorporated into concrete to produce green fiber-reinforced concrete (FRC). The present study has been conducted for facilitating the characterization of the tensile properties of macro fiber reinforced concrete (MFRC). A trilinear bond-slip model based on the shear-lag theory has first been refined by introducing a slip coefficient to consider different slip behaviors at the final pullout stages. Such a refined trilinear bond-slip model is suitable for describing the bond-slip behavior of the recycled macro fibers embedded in the cementitious matrix. The bond parameters are obtained through an inverse analysis, in which an improved particle swarm optimization algorithm (PSO) is used. The predicted force-end slip curves are compared with the pullout test results, and a good agreement is observed counterparts with the integral absolute error (IAE) ranging from 3.05% to 5.52%, demonstrating the feasibility of the proposed analytical model. A parametric study is finally conducted to examine the sensitivity of different parameters including the fiber geometries and bond properties on the pullout behavior of the macro fibers.

Hygrothermal effect on interfacial properties of CFRP-steel joint modified by nanosilica

The interface between the carbon fiber reinforced polymer (CFRP) reinforcement system and steel substrates may deteriorate in service environments. This study is concerned with the effect of moisture and temperature conditions on the interfacial performance of CFRP-steel joints using neat/modified adhesive. Tensile and shear tests were conducted on both unmodified adhesive specimens and those modified with nanosilica to assess the impact of nanoparticles. Water immersion tests were carried out on adhesive specimens with different nanosilica contents to determine the water absorption law of the adhesives at different immersion temperatures. The interfacial properties of CFRP-steel bonded joints were tested before and after hygrothermal aging. The results show that nanosilica significantly influences the mechanical properties of the adhesive, as well as CFRP-steel joints. In dry conditions, tensile and shear strengths, Young’s modulus and the elongation of adhesive are improved by increasing the nanosilica content up to about 1.4 wt%. A higher content of nanosilica reduces adhesive strength and modulus, while the elongation increases continuously with nanoparticles increasing to 7 wt%. The water absorption of the adhesive is significantly influenced by the content of nanosilica. More nanosilica particles lead to slower diffusion in adhesion and smaller saturated water absorption. A high immersion temperature speeds up the moisture diffusion, resulting in a larger moisture content and a more severe degradation in adhesive performance with the same immersion duration. Hygrothermal aging can be delayed by the addition of nanosilica with low content. The interfacial properties of CFRP-steel joints, including interfacial shear strength, load capacity and plasticity, are weakened by hygrothermal aging. Changing the main failure mode from cohesive failure to interfacial debonding may occur in CFRP-steel joints due to aging. The more severe deterioration is caused by longer immersion or a higher immersion temperature. However, the addition of nanosilica can enhance the durability of the aged joints in the long run by improving the water resistance, although peak shear stress decreases when the nanosilica content exceeds 1.4 wt%. The trilinear bond-slip model of reinforced adhesive joints may be reduced to a bilinear model by hygrothermal aging. The incorporation of nanosilica helps to mitigate the reduction in fracture energy due to water immersion at normal and high temperatures.

Experimental Study on Bond Behavior of Glass Textile Mesh in Earth-Based Matrix.

The bond behavior between the textile and the earth-based matrix determined the reinforcement effectiveness of the composite systems. This paper presented a pull-out experimental study on the glass textile mesh reinforced earth-based matrix. The bond behavior was studied using different development length, mesh spacing size and matrix thickness, with a total of 32 experimental specimens. The test results showed that the peak pull-out force had increased by 31.7% and 40.5% with 200 mm and 300 mm versus 100 mm development length, respectively. The 16 mm compared to 10 mm matrix thickness specimens had a high strength improvement (9.73%) because the elevated thickness had increased the matrix strength. However, the 20 mm versus 10 mm mesh spacing size specimens had achieved a slight reduction (5.72%) due to the reduction in the number of textiles along the weft direction. The failure mode shifted from pulling out, compound modes (both pulling out and textile rupture) to textile rupture mainly accompanied by elevated development length. In addition, we discussed the applicability of the trilinear bond-slip model on the earth-based matrix and proposed a method based on the fracture energy concept for estimating the effective development length, which could provide a reference for future research.

Numerical simulation of fully grouted rock bolts with or without faceplates based on the tri-linear bond-slip model

A difference scheme of the governing equation of the bolt-grout interface of the fully grouted rock bolt was derived based on the tri-linear bond-slip model, local equilibrium condition, and finite difference method. The corresponding solution formats of the fully grouted rock bolts with or without faceplates were proposed according to their different boundary conditions. Consequently, a numerical model of the fully grouted rock bolts with or without faceplates was established. This model is able to simulate the bonding, softening, and decoupling characteristics of the bolt-grout interface of the fully grouted rock bolts with or without faceplates subjected to the pullout load or rock deformation. The prediction results of this model agree well with the pullout test results, the calculation results of related scholars, and the analytical solutions, which proves its correctness. Then, the formulas of the support reaction force of the rock bolts with or without faceplates were derived according to their support mechanisms, and the support reaction force was applied during the iteration to simulate the bolt-rock interaction. This method is convenient for engineering applications owing to that it does not need to add additional degrees of freedom for rock bolts. The abovementioned model and method were incorporated into a self-developed FEM program and the effect of the initial deformation of the surrounding rock before bolt installation was considered, resulting in a numerical simulation program for fully grouted rock bolts with or without faceplates in underground caverns. Finally, this program was applied in a circular tunnel and the influences of the faceplate, bolt installation timing, bolt length, and bolt radius on the support performance of rock bolts were investigated. The following conclusions were obtained. 1) The faceplate can greatly improve the support effect. 2) The main failure mode of the rock bolts without faceplates is the shear damage at the bolt-grout interface, while the bolt pull-off is the dominant failure mode of the rock bolts with faceplates. 3) There is a critical value of bolt length. Increasing the bolt length within the critical value can significantly enhance the support effect, whereas increasing the bolt length beyond the critical value has little effect on the support effect. 4) Increasing the bolt radius can effectively enhance the support effect.

Fabric-to-cementitious matrix bond behavior in carbon fabric reinforced cementitious matrix (FRCM) composites with added short fibers

Fabric reinforced cementitious matrix (FRCM) composites are promising composite materials with useful properties, such as non-toxicity, fire resistance, corrosion resistance, and vapor permeability. However, the brittle failure mode, fabric efficiency, and tensile strength of FRCM composites require further improvement. Accordingly, the addition of short fibers to the matrix is proposed to improve the mechanical properties of FRCM composites, which are highly influenced by the fabric-to-cementitious matrix bond behavior. The objective of this study is to investigate the fabric-to-cementitious matrix bond behavior in carbon FRCM composites with added short fibers and to propose a method to evaluate the bond parameters. In total, 75 pullout specimens were designed to investigate the effects of short fiber type, short fiber volume content, and embedded length on the fabric-to-cementitious matrix bond behavior using double-sided pullout tests. The experimental results were evaluated in terms of the peak pullout force, displacement at peak pullout force, toughness, average bond strength, and initial stiffness. A closed-form solution was presented for the pullout force-displacement relationship based on a trilinear bond-slip model that accounted for the contribution of weft yarn. Furthermore, a method for the analytical extraction of bond parameters was proposed using the main characteristics of the experimental pullout force-displacement responses.

An Analytical Solution for Stress Transfer between a Broken Prestressing Wire and Mortar Coating in PCCP.

A prestressed concrete cylinder pipe (PCCP) consists of a concrete core, a steel cylinder, prestressing wires, and a mortar coating. Most PCCP failures are related to the breakage of prestressing wires. It is thus expected that the load-bearing capacity of PCCP is significantly affected by the length of the prestress loss zone and the stress distribution in the broken wire. Based on a tri-linear bond-slip model, the length of prestress loss zone and the stress transfer mechanism between a broken wire and a mortar coating are analysed in this paper. During the breaking (unloading) process of a prestressing wire, the interfacial bondline exhibits the following three stages: elastic stage, elastic-softening stage, and elastic-softening-debonding stage. The closed-form solutions for the interfacial slip, the interfacial shear stress, and the axial stress in the broken wire are derived for each stage. The solutions are verified by the finite element predictions. A parametric study is presented to investigate the effects of the size of the prestressing wires, the prestressing level, the interfacial shear strength, and the residual interfacial shear strength on the interfacial stress transfer. For an example PCCP with an inner diameter of 4 m, the length of prestress loss zone increases from 500 mm to 3300 mm as the radius of prestressing wire increases from 1 mm to 7 mm. It increases from 2700 mm to 7700 mm when the interfacial shear strength reduces from 3.94 MPa to 0.62 MPa and reduces from 13,200 mm to 7300 mm as the residual interfacial shear stress factor increases from 0.1 to 0.9.

Investigating the anchorage performance of full-grouted anchor bolts with a modified numerical simulation method

To reveal the failure mechanism of full-grouted bolting system, revised Pile elements were selected to numerically reveal the anchoring performance of full-grouted anchor bolts. A tri-linear bond-slip model was embedded in the Pile elements. A three-dimensional mining stope was created. A rectangular main roadway reinforced with full-grouted anchor bolts was simulated. Then, the retreat mining method was used to exploit the coal seam. The impact of buried depth, pillar size and shearing strength of the grout/rock contact surface was studied. It showed that the coal seam’s burial depth significantly influenced the anchorage performance of the anchor bolts. Moreover, increasing the shearing strength of the grout/rock contact surface was conductive to improving the anchorage performance of anchor bolts and preventing roadway convergence. Simulation results were compared against experimental laboratory test and in-situ observation outcome. It was conductive to revealing the anchorage mechanism of full-grouted anchor bolts under the in-situ condition.

Analytical modeling for the load-transfer behavior of stiffened deep cement mixing (SDCM) pile with rigid cap in layer soils

A new composite structure named stiffened deep cement mixing (SDCM) piles has recently been considered and applied in many geotechnical engineering projects. The SDCM pile was formed by inserting a stiffened core into the deep cement mixing (DCM) pile that has just finished construction, thereby combining the advantages of DCM piles and concrete piles. This study developed a load-transfer analytical approach for SDCM pile with rigid cap in layer soils from the theoretical solution view. Herein, the nonlinear mechanical behaviors of the DCM pile–soil and DCM pile–stiffened core interfaces were characterized by a tri-linear bond-slip model, and the action of soil on the pile end was simulated by an elastic-perfectly plastic model. Three-dimensional finite element simulations were conducted for SDCM piles embedded in homogeneous soil and double-layer soils. The reasonable matches between the predictions and the results from FE simulations and physical model tests confirmed the applicability of the theoretical approach. The full-range load-transfer behavior and the bearing performance of SDCM piles were further discussed. Parametric studies were finally conducted, providing insights into the design practice of SDCM piles.

Experimental, Analytical and Numerical Studies of Interfacial Bonding Properties between Silane-Coated Steel Fibres and Mortar

A systematic investigation of the effects of silane coatings on steel fibre–mortar interfacial bond properties was conducted, combining pullout tests, analytical solutions, and meso-scale FE simulations. Nine silane coatings were tested, and their effects were evaluated by 30 single fibre pullout tests. They were found to increase the peak force and energy consumption up to 5.75 times and 2.48 times, respectively. Closed-form analytical solutions for pullout load, displacement, and interfacial stress distribution during the whole pullout process were derived based on a tri-linear bond-slip model, whose parameters were calibrated against the pullout tests. Finally, the calibrated bond-slip models were used to simulate the pullout tests and complex failure of multi-fibre specimens in mesoscale finite element models. Such an approach of combining pullout tests, analytical solutions, and mesoscale modelling provides a reliable way to investigate the effects of fibre–mortar interfacial properties on the mechanical behaviour of steel fibre reinforced concrete members in terms of structural strength, stiffness, ductility, and failure mechanisms.

Analysis of Deformation Characteristics of Fully Grouted Rock Bolts Under Pull-and-Shear Loading

A new analytical approach able to predict the mechanical behavior of fully grouted rock bolts subjected to pull-and-shear load is been proposed. The elastic theory of a semi-infinite length beam and approximate differential equation of the deflection curve (elastic and elastoplastic) are employed to analyze the lateral behavior of a bolt under surrounding rock pressures. Bolt axial behavior is based on a realistic tri-linear bond-slip model with residual bond strength at the grout–bolt interface. According to the Tresca yield criterion, important failure parameters such as shear displacement, tangent direction, tensile displacement, and tensile force can be determined via the analytical approach while the shear force and other basic parameters are provided. Results of the proposed analytical approach for 0°, 20°, 40°, 60°, and 90° displacing angles correlate well with experimental test results. Parametric analysis of both the rock and bolt mechanical behavior are also carried out using this new analytical approach.

Three-dimensional axisymmetric analytical method for pull-out behaviour of adhesive anchors in concrete

The importance of precise prediction of the pull-out behaviour of adhesive anchors in concrete has been emphasised by several researchers. It is known that the pull-out problem of anchors is a three-dimensional (3D) one in nature. However, most of the current analytical studies are limited to one-dimensional (1D) analysis and only few 3D studies are reported in the literature. This paper develops a 3D analytical method for evaluating the pull-out behaviour of adhesive anchors in concrete. In the method, the debonding failure at the anchor-adhesive interface and the concrete cone failure are considered for two cases of boundary conditions. Based on a tri-linear bond-slip model, two sets of closed-form analytical solutions are derived for evaluating the stress fields and the pull-out load throughout the entire loading process. Finally, seven sets of experimental data collected from the literature are used to verify the validity of the analytical method. It is shown that the presented analytical solution can evaluate the interfacial shear stress distribution, the axial stress distribution in the anchor, and the maximum pull-out load of various adhesive anchor systems with reasonable accuracy. It is also found that, when Poisson’s effect is neglected, the closed-form solutions can be reduced to the previous 1D solutions. Although this study is conducted within the context of adhesive anchors, the analytical method is applicable to similar anchorage systems such as bar-to-concrete or fibre-to-matrix bonded anchorages.

Bond-slip modeling of a CMC rockbolt element using 2D-DDA method

The bonding condition at the rock and rockbolt interface is one of the most important factors to determine the load transfer mechanism of a CMC rockbolt element. The two-dimensional Discontinuous Deformation Analysis (2D-DDA) method is used in this paper to investigate the pullout performance of the CMC rockbolt element which is modeled as three components, i.e. the rock, the rockbolt and the mortar. The material properties used in the numerical models are calibrated against the experiments results. The simulated results show that a bond stress versus slip displacement curve of the CMC rockbolt element is exhibiting three stages which could be represented by a trilinear bond-slip model. Parametric studies have been carried out to investigate the effects of the confining pressure and those of the geometry configuration of the rockbolt ribs on the bond stress versus slip displacement curves and the crack propagations in the mortar. It is found that the maximum bond strength and the residual bond strength increase with the increase of confining pressure. Under lower confining pressure, the rib face angle controls the dilation of rock blocks. The obtained key parameters of the trilinear bond – slip models can be used to simulate the bond behavior between the rockbolt and rock interface in pullout test. The nodal axial forces and nodal bond force distributions along the rockbolt could be curve fitted using exponential models. The obtained parameters of the exponential models can be used for engineering practice under similar conditions.

Three-dimensional analytical model for the pull-out response of anchor-mortar-concrete anchorage system based on interfacial bond failure

The interfacial bond behavior plays a significant role in determining the load transfer performance of anchor systems. Numerous analytical models have been proposed to investigate the pull-out behavior of grouted anchors, but no closed-form three-dimensional solution has been derived for the pull-out response of anchor systems with respect to interfacial bond failure. By considering the bond failure at the anchor-mortar interface, this paper presents a three-dimensional analytical model for predicting the pull-out response of grouted anchors based on a tri-linear bond-slip model. Specifically, the closed-form expressions are derived for the axial displacement, axial stress, and shear stress of the anchor and concrete, the load-displacement relationship of the anchor, and the interfacial shear stress at various possible pull-out stages. Furthermore, the load-displacement relationships and interfacial shear stress distributions are analyzed for different bond lengths during the whole pull-out process. The validity of the three-dimensional model is verified with experimental results collected from the literature. Through a systematic parametric study, the effect of bond length on the ultimate load and load-displacement response is investigated with the proposed model. It is shown that the ultimate load increases with the increase of bond length significantly before a critical bond length is reached but thereafter at a smaller and steady rate. Moreover, a longer bond length improves the ductility of the anchorage and the snapback phenomenon in the load-displacement response is dependent on the bond length, while the intensity of snapback increases with an increase in bond length. The proposed model is capable of better understanding the debonding mechanism and can be employed by engineers and researchers to predict the ultimate load capacity and load-displacement response of anchor systems.

Whole-process Bond Characteristics of FRP-to-concrete Joint under Pressure

Lateral anchoring can effectively inhibit the premature debonding of FRP (Fiber-Reinforced Polymer) plate bonds to concrete. To effectively improve the efficiency of reinforcement, the bond characteristics of FRP-to-concrete joints under pressure through the entire debonding process were analyzed via a theoretical model, experimental evaluation, and parameter studies. The results show that the load-slip behavior of a bonded joint features an elastic stage, an elastic-softening stage, an elastic-softening-residual stage, a softening-residual stage and a residual stage. Moreover, the trilinear bond-slip model reveals changes in interface bonding properties under pressure. The experimental analysis of the load-slip relationship and bond stress distribution prove the accuracy of the theoretical model. Both load capacity and slip increase with increasing bond length or lateral pressure, while increasing the plate stiffness results in an increased load capacity and a reduction in ductility.

Interface behavior of tensioned bars embedded in cement-soil mixtures

The overall performance of reinforced cement-stabilized soils depends significantly on the interface bond mechanisms that develop between the reinforcement and the surrounding cement-soil mixture. A laboratory experimental investigation based on uniform design theory was carried out to characterize the interface behavior of deformed bars embedded in cement-admixed soils. The study focused on the influence of cement content, water content and curing duration on the interface response. The interface bond strength of reinforced cement-soil mixture, as measured in pullout tests, was found to be proportional to the strength of cement-soil matrix, as obtained from unconfined compression tests. A simplified trilinear bond-slip model was developed as part of this study, which when properly calibrated was found to be capable of characterizing the bar-mixture interface shear response. Correlations were obtained to relate the interface bond strength with the three influence factors investigated in this study. The trends obtained on the influence of each factor on the interface bond resistance provided insights that were suitable to guide current design and construction practice of reinforced cement-soil mixture. The results and testing protocols presented in this study facilitated the understanding for interface shear mechanism between deformed bar and cement-soil mixture, and are expected to provide adequate means to satisfy the current lack of bar-mixture interface bond parameters in design specification for reinforced soil mixing structures.

A theoretical solution for the pullout properties of a single FRP rod embedded in a bond type anchorage

ABSTRACTThis paper proposes a theoretical solution for predicting the pullout properties of a single fiber-reinforced polymer (FRP) rod embedded in a bond type anchorage based on a trilinear bond–slip model. The radial variation of the shear stress and reaction of the steel sleeve are considered in the solution. Pullout procedure with elastic, elastic-softening, elastic-softening-debonding, pure softening, softening-debonding, and debonding stages, as well as the corresponding critical stages, are analyzed. In this theoretical solution, the maximum pullout load, shear stress along the rod–grout interface, axial tensile stress of the FRP rod, and load–slip relationship are derived with explicit formulations. Effective bond length of bond type anchorage is also discussed. The solution is validated against experimental results available in literature. The theoretical solution reveals that the anchorage may attain its maximum pullout load in the elastic-softening, pure softening, or elastic-softening-debonding stage. Moreover, the effects of embedded length, ultimate shear stress, and residual shear stress on maximum pullout load closely related with the stage in which the anchorage attains its maximum pullout load. However, the effect of radius of FRP rod on the maximum pullout load increases with the embedded length, no matter in which stage the anchorage attains its maximum pullout load.

Double lap shear test on steel fabric reinforced cementitious matrix (SFRCM)

The present work deals with the experimental characterization of the mechanical bond behaviour of a galvanized steel fabric reinforced cementitious matrix (SFRCM) laminated on concrete support. The specimens, made of two low strength concrete blocks connected with a galvanized steel fabric embedded in a geo-polymeric mortar layer, have been tested according to double lap test (DLT) set-up. Six different groups of specimens have been tested varying both the lamination length and the steel fabric density. In order to reproduce the load-slip or bond-slip curves, a tri-linear bond slip model together with its parameters identification has been proposed.For some specimens, the slip profile and the slip distribution have been analysed and split into the substrate laminate slip and inner laminate layers slip. This distinction has been used as a measure of the fabric-matrix compatibility. In addition, the effect induced by the rigid blocks rotation occurred during the DLT has been argued. The DIC optical system monitoring has been used to asses both the force-slip distribution and the crack opening displacement (COD).

Bond characteristics of CFRP-to-steel joints

Carbon Fiber Reinforced Polymer (CFRP) composites have a large potential for strengthening and retrofitting steel parts but due to their premature debonding from steel, further data and research are still required for wider application in such situations. In the present paper, the bond characteristics of CFRP-to-steel joints in pull-pull loaded conditions were studied. Monotonic loading of the double strap joints with different bond lengths was applied and the failure modes and interfacial bond-slip curves were obtained. A tri-linear bond-slip model is proposed and it was derived from the experimental data. A closed-form solution approach is also proposed based on the tri-linear bond-slip model. The strength of the CFRP-to-steel interface, the distribution of the relative displacements between bonded materials, the strains developed in the CFRP laminate and the bond stresses along the interface are reported and the closed-form solution is compared with the experimental results. Two cases are selected for presentation: (i) one with the bond length greater than the effective bond length; and, inversely, (ii) one with bond length which is shorter than the effective bond length. The results predicted by the closed-form solutions are shown to be accurate enough when compared to the experiments.

Analysis of the debonding process of CFRP-to-timber interfaces

The use of Fiber Reinforced Polymers (FRP) in the strengthening of timber structures is quite recent and few studies have discussed the debonding between these materials. The analysis of the Mode II debonding process between FRP composites and timber elements may be of great importance because this mode is predominant in the case, for instance, of the bending of beams. Knowing the appropriate bond-slip model to use on the estimation of the performance of FRP-to-timber interfaces is greatly relevant. Under such circumstances, a detailed knowledge of all the states that CFRP-to-timber interfaces are subjected to is important as well. The current work gives answers to these aspects proposing an analytical solution based on a tri-linear bond-slip model that is capable of describing precisely the full-range debonding behavior of FRP-to-timber interfaces. Thus, the purpose of this study is to contribute to existing knowledge with an analytical solution capable of describing the full-range debonding process between a FRP composite and a substrate. The analytical solutions herein proposed are also compared with the results obtained from several experiments based on single-lap shear tests. Comparisons at different load levels and different bonded lengths are presented. The slips, strains in the CFRP composite and bond stress distributions within the bonded interface are emphasized in the text. The complete load-slip response of CFRP-to-timber interface is also analyzed. Each state of the debonding process is described and each one is identified in the load-slip curve.