Investigation of FRP and SFRC Technologies for Efficient Tunnel Reinforcement Using the Cohesive Zone Model

Amid urbanization and the continuous expansion of transportation networks,the necessity for tunnel construction and maintenance has become paramount.Addressing this need requires the investigation of efficient,economical,and robust tunnel reinforcement techniques.This paper explores fiber reinforced polymer(FRP)and steel fiber reinforced concrete(SFRC)technologies,which have emerged as viable solutions for enhancing tunnel structures.FRP is celebrated for its lightweight and high-strength attributes,effectively augmenting load-bearing capacity and seismic resistance,while SFRC’s notable crack resistance and longevity potentially enhance the performance of tunnel segments.Nonetheless,current research predominantly focuses on experimental analysis,lacking comprehensive theoretical models.To bridge this gap,the cohesive zone model(CZM),which utilizes cohesive elements to characterize the potential fracture surfaces of concrete/SFRC,the rebar-concrete interface,and the FRP-concrete interface,was employed.A modeling approach was subsequently proposed to construct a tunnel segment model reinforced with either SFRC or FRP.Moreover,the corresponding mixed-mode constitutive models,considering interfacial friction,were integrated into the proposed model.Experimental validation and numerical simulations corroborated the accuracy of the proposed model.Additionally,this study examined the reinforcement design of tunnel segments.Through a numerical evaluation,the effectiveness of innovative reinforcement schemes,such as substituting concrete with SFRC and externally bonding FRP sheets,was assessed utilizing a case study from the Fuzhou Metro Shield Tunnel Construction Project.

Numerical simulation of the mechanical behavior of superconducting tape in conductor on round core cable using the cohesive zone model

Cables composed of rare-earth barium copper oxide(REBCO)tapes have been extensively used in various superconducting devices.In recent years,conductor on round core(CORC)cable has drawn the attention of researchers with its outstanding current-carrying capacity and mechanical properties.The REBCO tapes are wound spirally on the surface of CORC cable.Under extreme loadings,the REBCO tapes with layered composite structures are vulnerable,which can lead to degradation of critical current and even quenching of superconducting devices.In this paper,we simulate the deformation of CORC cable under external loads,and analyze the damage inside the tape with the cohesive zone model(CZM).Firstly,the fabrication and cabling of CORC are simulated,and the stresses and strains generated in the tape are extracted as the initial condition of the next step.Then,the tension and bending loads are applied to CORC cable,and the damage distribution inside the tape is presented.In addition,the effects of some parameters on the damage are discussed during the bending simulations.

COHESIVE ZONE FINITE ELEMENT-BASED MODELING OF HYDRAULIC FRACTURES

Hydraulic fracturing is a powerful technology used to stimulate fluid production from reservoirs. The fully 3-D numerical simulation of the hydraulic fracturing process is of great importance to the efficient application of this technology, but is also a great challenge because of the strong nonlinear coupling between the viscous flow of fluid and fracture propagation. By taking advantage of a cohesive zone method to simulate the fracture process, a finite element model based on the existing pore pressure cohesive finite elements has been established to investigate the propagation of a penny-shaped hydraulic fracture in an infinite elastic medium. The effect of cohesive material parameters and fluid viscosity on the hydraulic fracture behaviour has been investigated. Excellent agreement between the finite element results and analytical solutions for the limiting case where the fracture process is dominated by rock fracture toughness demonstrates the ability of the cohesive zone finite element model in simulating the hydraulic fracture growth for this case.

CRACK PROPAGATION IN POLYCRYSTALLINE ELASTIC-VISCOPLASTIC MATERIALS USING COHESIVE ZONE MODELS

Cohesive zone model was used to simulate two-dimensional plane strain crack propagation at the grain level model including grain boundary zones. Simulated results show that the original crack-tip may not be separated firstly in an elastic-viscoplastic polycrystals. The grain interior＇s material properties （e.g. strain rate sensitivity） characterize the competitions between plastic and cohesive energy dissipation mechanisms. The higher the strain rate sensitivity is, the larger amount of the external work is transformed into plastic dissipation energy than into cohesive energy, which delays the cohesive zone rupturing. With the strain rate sensitivity decreased, the material property tends to approach the elastic-plastic responses. In this case, the plastic dissipation energy decreases and the cohesive dissipation energy increases which accelerates the cohesive zones debonding. Increasing the cohesive strength or the critical separation displacement will reduce the stress triaxiality at grain interiors and grain boundaries. Enhancing the cohesive zones ductility can improve the matrix materials resistance to void damage.

IMPROVED COHESIVE ZONE MODEL AND ITS APPLICATION IN INTERFACE CONTACT ANALYSIS

An improved interface cohesive zone model is developed for the simulation of interface contact, under mixed-mode loading. A new debonding initiation criterion and propagation of debonding law, taking into account the pressure stress influence on contact shear strength, is proposed. The model is implemented in a finite-element program using subroutine VUINTER of ABAQUS Explicit. An edge-notch four-point bending process and laminated vibration damping steel sheet punch forming test are simulated with the improved model in ABAQUS Explicit. The numerical predictions agree satisfactorily with the corresponding experimental results.

A novel method for modeling the phase change of iron ore particles in the cohesive zone of a blast furnace

Cohesive zone plays a vital role in the stable operation of a blast furnace(BF),yet the complex phase change process of iron ore particles in this zone is still not well understood.In this study,a novel one-dimensional(1D)unsteady phase change model was developed to elucidate the heat transfer and melting mechanisms of iron ore particles.After model validation,the effects of several key operating parameters(e.g.,particle diameter,gas velocity,initial temperature)on the phase change behavior of iron ore particles were analyzed,and the joint effect of multiple parameters was discussed.The results show that larger-sized iron ore particles possess lower specific surface areas,which in turn reduces their convective heat absorption capacity.Consequently,the distance from the solid-liquid phase interface to the particle surface increases,thereby slowing down the movement of the phase interface and pro-longing the melting duration of the particles.Increasing the gas velocity and the initial temperature does not have a significant impact on reducing the duration of the complete melting process.Under the specified conditions,it is observed that increasing the gas velocity by 3-fold and 9-fold results in a reduction of the melting duration by 2.4%and 8.3%,respectively.Elevating the initial temperature of iron ore particles results in a decrease in the core-to-surface temperature difference,a slower heating rate,and a shorter duration to achieve melting.Among the factors affecting the melting process,the particle diameter is found to be the most significant in terms of the liquid phase precipitation,mushy zone thickness,and core-to-surface temperature difference of iron ore particles.

Effect of atmosphere and basicity on softening-melting behavior of primary slag formation in cohesive zone

The softening-melting characteristics of ferrous burden play a crucial role in the thickness and position of the cohesive zone.The influence of the basicity and experimental atmosphere on the softening-melting behavior of primary slag under slag-coke interaction was investigated using in situ visualization method.The mechanism was analyzed using the FactSage software,X-ray diffraction,and electron probe microanalysis.The softening and melting temperatures of the samples increased with increasing basicity under different atmospheres.The difference between softening and melting temperatures is smaller in a H_(2) atmosphere than in a CO atmosphere;in H_(2) atmosphere,the range of softening zone in the cohesive zone was significantly thinner.The formed low-melting-point FeO-bearing phases decrease when H_(2) was used as the reducing agent.In addition,according to FactSage calculations,the high content of metallic iron reduced in the H_(2) atmosphere raised the softening temperature of the primary slag.It also narrowed and moved downward the cohesive zone due to an increase in softening and melting temperatures.Meanwhile,the increase in basicity promoted the decrease in liquid ratio and improved the permeability of cohesive zone.

Softening and melting behaviors of ferrous burden in hydrogen-rich blast furnace cohesive zone

The changes in the softening and melting behaviors of ferrous burden in the cohesive zone and the characteristics of the slag–iron–coke interface in a blast furnace were investigated by simulating an actual blast furnace under hydrogen-rich conditions.According to the variation in the transient shrinkage of the burden under different atmospheres,the shrinkage start temperature of the sinter was higher than that of the pellets.The negative shrinkage rate of the pellets was greater than that of the sinter.Additionally,the softening start temperature in the blast furnace decreased under hydrogen-rich conditions,giving the blast furnace a broader range of softening zones.The softening start temperatures of the pellets and sinter decreased from 1102 to 949℃ and 1152 to 1080℃,respectively.The hydrogen-rich traditional blast furnace conditions narrowed the melting zone temperature range and shifted it toward the high-temperature zone,significantly improving the burden layer permeability.However,under the hydrogen-rich oxygen blast furnace conditions,there were a decrease in the melting start temperature,a shift of the melting zone location to the low-temperature zone,and an increase in the burden layer permeability and pressure difference.A comparison of the slag–iron–coke interface characteristics under different atmospheric conditions showed that the carbon content in metallic iron decreased under hydrogen-rich traditional blast furnace conditions compared with traditional blast furnace conditions.Contrastingly,under hydrogen-rich oxygen blast furnace conditions,the carbon content in metallic iron increased compared with oxygen blast furnace conditions.These findings provide guidance for the development of low-carbon ironmaking processes in blast furnaces.

Finite Element Simulations of the Localized Failure and Fracture Propagation in Cohesive Materials with Friction

Strain localization frequently occurs in cohesive materials with friction(e.g.,composites,soils,rocks)and is widely recognized as a fundamental cause of progressive structural failure.Nonetheless,achieving high-fidelity simulation for this issue,particularly concerning strong discontinuities and tension-compression-shear behaviors within localized zones,remains significantly constrained.In response,this study introduces an integrated algorithmwithin the finite element framework,merging a coupled cohesive zone model(CZM)with the nonlinear augmented finite elementmethod(N-AFEM).The coupledCZMcomprehensively describes tension-compression and compressionshear failure behaviors in cohesive,frictional materials,while the N-AFEM allows nonlinear coupled intraelement discontinuities without necessitating extra nodes or nodal DoFs.Following CZM validation using existing experimental data,this integrated algorithm was utilized to analyze soil slope failure mechanisms involving a specific tensile strength and to assess the impact of mechanical parameters(e.g.,tensile strength,weighting factor,modulus)in soils.

Influence of Cohesive Zone Shape on Solid Flow in COREX Melter Gasifier by Discrete Element Method

Based on the principle of discrete element method （DEM）, a 2D slot model of a COREX melter gasifier was established to analyze the influence of cohesive zone shape on solid flow, including mass distribution, velocity distribution, normal force distribution and porosity distribution at a microscopic level. The results show that the co- hesive zone shape almost does not affect the particle movement in the upper shaft and deadman shape. The particles in the lower central bottom experience large normal force to support the particles above them, while particles around the raceway and in the fast flow zone exhibit weak force network. The porosity distribution was also examined under three kinds of cohesive zones. Like the velocity distribution, the whole packed bed can be divided into four main re- gions. With the increase of cohesive zone position, the low porosity region located in the root of cohesive zone increa- ses. And the porosity distribution becomes asymmetric in the case of biased cohesive zone.

Isogeometric cohesive zone model for thin shell delamination analysis based on Kirchhoff-Love shell model

We present a cohesive zone model for delamination in thin shells and composite structures.The isogeometric(IGA)thin shell model is based on Kirchhoff-Love theory.Non-Uniform Rational B-Splines(NURBS)are used to discretize the exact mid-surface of the shell geometry exploiting their C 1-continuity property which avoids rotational degrees of freedom.The fracture process zone is modeled by interface elements with a cohesive law.Two numerical examples are presented to test and validate the proposed formulation in predicting the delamination behavior of composite structures.

Progressive fragmentation of granular assemblies within rockslides: Insights from discrete-continuous numerical modeling

Rock fragmentation plays a critical role in rock avalanches,yet conventional approaches such as classical granular flow models or the bonded particle model have limitations in accurately characterizing the progressive disintegration and kinematics of multi-deformable rock blocks during rockslides.The present study proposes a discrete-continuous numerical model,based on a cohesive zone model,to explicitly incorporate the progressive fragmentation and intricate interparticle interactions inherent in rockslides.Breakable rock granular assemblies are released along an inclined plane and flow onto a horizontal plane.The numerical scenarios are established to incorporate variations in slope angle,initial height,friction coefficient,and particle number.The evolutions of fragmentation,kinematic,runout and depositional characteristics are quantitatively analyzed and compared with experimental and field data.A positive linear relationship between the equivalent friction coefficient and the apparent friction coefficient is identified.In general,the granular mass predominantly exhibits characteristics of a dense granular flow,with the Savage number exhibiting a decreasing trend as the volume of mass increases.The process of particle breakage gradually occurs in a bottom-up manner,leading to a significant increase in the angular velocities of the rock blocks with increasing depth.The simulation results reproduce the field observations of inverse grading and source stratigraphy preservation in the deposit.We propose a disintegration index that incorporates factors such as drop height,rock mass volume,and rock strength.Our findings demonstrate a consistent linear relationship between this index and the fragmentation degree in all tested scenarios.

Constitutive Behavior of the Interface between UHPC and Steel Plate without Shear Connector:From Experimental to Numerical Study

The application of ultra-high performance concrete(UHPC)as a covering layer for steel bridge decks has gained widespread popularity.By employing a connection without a shear connector between the steel plate and UHPC,namely,the sandblasted interface and the epoxy adhesive with sprinkled basalt aggregate interface,the installation cannot only be simplified but also the stress concentration resulting from the welded shear connectors can be eliminated.This study develops constitutive models for these two interfaces without shear connectors,based on the interfacial pull-off and push-out tests.For validation,three-point bending tests on the steel-UHPC composite plates are conducted.The results indicated that the proposed bilinear traction-separation model for the sandblasted interface and the trapezoidal traction-separation model for the epoxy adhesive with sprinkled basalt aggregate interface can generally calibrate the interfacial behavior.However,the utilization of the experimentally determined pure shear strength underestimates the load-carrying capacity of the composite plates in the case of three-point bending tests.By recalling the Mohr-Coulomb criterion,this underestimation is attributed to the enhancement of the interface shear strength by the presence of normal stress.

Effect of intermittent joint distribution on the mechanical and acoustic behavior of rock masses

The mechanical characteristics and acoustic behavior of rock masses are greatly influenced by stochastic joints.In this study,numerical models of rock masses incorporating intermittent joints with different numbers and dip angles were produced using the finite element method(FEM)with the intrinsic cohesive zone model(ICZM).Then,the uniaxial compressive and wave propagation simulations were performed.The results indicate that the joint number and dip angle can affect the mechanical and acoustic properties of the models.The uniaxial compressive strength(UCS)and wave velocity of rock masses decrease monotonically as the joint number increases.However,the wave velocity grows monotonically as the joint dip angle increases.When the joint dip angle is 45°–60°,the UCS of the rock mass is lower than that of other dip angles.The wave velocity parallel to the joints is greater than that perpendicular to the joints.When the dip angle of joints remains unchanged,the UCS and wave velocity are positively related.When the joint dip angle increases,the variation amplitude of the UCS regarding the wave velocity increases.To reveal the effect of the joint distribution on the velocity,a theoretical model was also proposed.According to the theoretical wave velocity,the change in wave velocity of models with various joint numbers and dip angles was consistent with the simulation results.Furthermore,a theoretical indicator(i.e.fabric tensor)was adopted to analyze the variation of the wave velocity and UCS.

Impact Analysis of Microscopic Defect Types on the Macroscopic Crack Propagation in Sintered Silver Nanoparticles

Sintered silver nanoparticles(AgNPs)arewidely used in high-power electronics due to their exceptional properties.However,the material reliability is significantly affected by various microscopic defects.In this work,the three primary micro-defect types at potential stress concentrations in sintered AgNPs are identified,categorized,and quantified.Molecular dynamics(MD)simulations are employed to observe the failure evolution of different microscopic defects.The dominant mechanisms responsible for this evolution are dislocation nucleation and dislocation motion.At the same time,this paper clarifies the quantitative relationship between the tensile strain amount and the failure mechanism transitions of the three defect types by defining key strain points.The impact of defect types on the failure process is also discussed.Furthermore,traction-separation curves extracted from microscopic defect evolutions serve as a bridge to connect the macro-scale model.The validity of the crack propagation model is confirmed through tensile tests.Finally,we thoroughly analyze how micro-defect types influence macro-crack propagation and attempt to find supporting evidence from the MD model.Our findings provide a multi-perspective reference for the reliability analysis of sintered AgNPs.

3D Cohesive Finite Element Minimum Invasive Surgery Simulation Based on Kelvin‑Voigt Model

Minimally invasive surgery is an important technique used for cytopathological examination.Recently,multiple studies have been conducted on a three-dimensional(3D)puncture simulation model as it can reveal the internal deformation state of the tissue at the micro level.In this study,a viscoelastic constitutive equation suitable for muscle tissue was derived.Additionally,a method was developed to define the fracture characteristics of muscle tissue material during the simulation process.The fracture of the muscle tissue in contact with the puncture needle was simulated using the cohesive zone model and a 3D puncture finite element model was established to analyze the deformation of the muscle tissue.The stress nephogram and reaction force under different parameters were compared and analyzed to study the deformation of the biological soft tissue and guide the actual operation process and reduce pain.

fmax and fault zone property of Lushan earthquake of 20 April 2013,Sichuan,China

In this study, we determined fnax from near- field accelerograms of the Lushan earthquake of April 20, 2013 through spectra analysis. The result shows that the values of fmax derived from five different seismography stations are very close though these stations roughly span about 100 km along the strike. This implies that the cause offmax is mainly the seismic source process rather than the site effect. Moreover, according to the source-cause model of Papageorgiou and Aki （Bull Seism Soc Am 73：693-722, 1983）, we infer that the cohesive zone width of the rupture of the Lushan earthquake is about 204 with an uncertainty of 13 m. We also find that there is a significant bulge between 30 and 45 Hz in the amplitude spectra of accel- erograms of stations 51YAL and 51QLY, and we confirm that it is due to seismic waves＇ reverberation of the sedi- mentary soil layer beneath these stations.

Separation work analysis of cohesive law and consistently coupled cohesive law

An appropriate coupled cohesive law for predicting the mixed mode failure is established by combining normal separation and tangential separation of surfaces in the cohesive zone model （CZM） and the cohesive element method. The Xu-Needleman exponential cohesive law with the fully shear failure mechanism is one of the most popular models. Based on the proposed consistently coupled rule/principle, the Xu-Needleman law with the fully shear failure mechanism is proved to be a non-consistently coupled cohesive law by analyzing the surface separation work. It is shown that the Xu-Needleman law is only valid in the mixed mode fracture when the normal separation work equals the tangential separation work. Based on the consistently coupled principle and the modification of the Xu-Needleman law, a consistently coupled cohesive （CCC） law is given. It is shown that the proposed CCC law has already overcome the non-consistency defect of the Xu-Needleman law with great promise in mixed mode analyses.

A Dugdale model based geometrical amplifier enables the measurement of separation-to-failure for a cohesive interface

Regardless of all kinds of different formulae used for the traction-separation relationship in cohesive zone modeling,the peak tractionσ_m and the separation-to-failureδ_0(or equivalently the work-to-separationΓ) are the primary parameters which control the interfacial fracture behaviors. Experimentally,it is hard to determine those quantities,especially forδ_0,which occurs in a very localized region with possibly complicated geometries by material failure.Based on the Dugdale model,we show that the separation-to-failure of an interface could be amplified by a factor of L/r_p in a typical peeling test,where L is the beam length and r_p is the cohesive zone size.Such an amplifier makesδ_0 feasible to be probed quantitatively from a simple peeling test. The method proposed here may be of importance to understanding interfacial fractures of layered structures,or in some nanoscale mechanical phenomena such as delamination of thin films and coatings.

Mesoscale Modeling of Hooked-End Steel Fiber Reinforced Concrete under Uniaxial Compression Using Cohesive Elements

Based on the cohesive zone model, the 2D mesostructures were developed for numerical studies of multi-phase hooked-end steel fiber reinforced concrete under uniaxial compression. The zero-thickness cohesive interface elements were inserted within the mortar, on interfaces of mortar and aggregates and interfaces of mortar and fibers to simulate the failure process of fiber reinforced concrete. The results showed that the numerical results matched well the experimental results in both failure modes and stress-strain behavior. Hooked-end steel fiber reinforced concrete exhibited ductile failure and maintained integrity during a whole failure process. Compared with normal concrete, HES fiber reinforced concrete was greater stiffness and compressive strength;the descending branch of the stress-strain curve was significantly flatter;the residual stress was higher.