Stress-strain Model Research Articles

Stress–Strain Model for Geopolymer Mortar under Active Confinement

A stress–strain model is developed for geopolymer mortar subjected to uniaxial compressive loading with active confinement. The model was developed using the triaxial test carried out on cylindrical geopolymer mortar samples cast with different weight percentages of slag and fly ash. The samples were tested under four levels of confining pressures (i.e., 0, 5, 10, and 15 MPa) to study the effect of confining pressure on peak stress, peak strain, volume change, modulus of elasticity, and Poisson’s ratio. The stress–strain behavioral model for geopolymer mortar together with the functional relationship for model parameters with confinement ratios is developed. The developed strain–strain model shows good agreement with the experimental results. Further, the modulus of elasticity and Poisson’s ratio are linearly varied with confining pressure. Also, the normalized volumetric strain factor increases linearly with the compressive strength. The obtained experimental results demonstrate significant improvement in strength and ductility due to confinement for geopolymer mortar.

Effect of nano-SiO2 modified recycled coarse aggregate on the mechanical properties of recycled concrete

Improving the performance of the interface between old mortar and recycled coarse aggregate (RCA) is a hot topic and important to enhance the properties of recycled aggregate concrete (RAC). In this paper, the RCA was soaked by nano-SiO2 (NS-RCA) then the water absorption and crushing index of NS-RCA were investigated. The mechanical properties, such as compressive strength, flexural strength, and elastic modulus of RAC prepared by NS-RCA (NS-RAC) were studied. The Thermogravimetric and Differential Thermal Analysis (TG-DTA) and scanning electron microscopy (SEM) were applied to analyze the properties of the interface transition zone (ITZ) around unmodified RAC and NS-RAC. A modified stress–strain model of NS-RAC was proposed considering the concentration of nano-SiO2 and soaking time. The testing results showed that the concentration of nano-SiO2 and soaking time had significant effects on the strength and durability of RCA and the mechanical properties of RAC. The 2% concentration of nano-SiO2 and 48 h soaking time had the best modification effect on RCA. The compressive strength, flexural strength, and elastic modulus of NS-RAC with best modification were 31.8%, 33.2%, and 89.6% higher than those of unmodified RAC respectively. The TG-DTA and SEM analyses indicated that NS-RAC had the denser microstructure of ITZ. This study is conducive to enrich the knowledge about using NS-RAC and supplying guidance for its mix design.

Stress-strain model of austenitic stainless steel for pressure vessel design

Stress-strain model of austenitic stainless steel for pressure vessel design

Effects of fibre wrapping degree and ratio on the tensile properties of carbon FRP-steel hybrid reinforcements

The aim of this study is to develop carbon fibre reinforced polymer (CFRP)-steel hybrid reinforcements that are more cost effective than CFRP reinforcements, resistant to external influences, have low creep, high modulus of elasticity, high tensile strength and high ductility. In this context, hybrid reinforcements were produced by winding epoxy impregnated carbon fibre on ribbed steel reinforcements with diameters of 8, 10 and 12 mm at 3 different angles (15, 30 and 45°) and 3 different layer thicknesses (from 1 layer to 3 layers) by filament winding method. In the study, the effect of reinforcement diameter, fibre ratio in the reinforcement (η) and fibre wrapping angle on hybrid reinforcement, yield and tensile stress, modulus of elasticity, energy dissipation capacity and ductility were investigated by tensile tests.As a result of the study, the tensile properties of the reinforcements hybridised by filament winding method improved more than the reinforcements hybridised by other methods (pultrusion, braidtrusion). Modulus of elasticity of the reinforcements developed by this method was 6%–38% higher than the other hybrid reinforcements and the energy dissipation capacity under maximum force was 5%–114% higher. In addition, the fibre ratio between 9% and 32% in specimens with 15° fibre winding angle improved the maximum tensile stress of the steel reinforcement by 3%–35% on average, while the specimens with 30 and 45° FRP winding angle had almost no contribution. It was observed that for the hybrid reinforcement to exhibit very linear behaviour, the fibre ratio (η) should be minimum 0.13 ≤ η and 0.29 ≤ η for the reinforcements with 15 and 30° wrap angle, respectively. The study also includes a theoretical stress-strain model to be in good agreement with the experimental results.

Investigating two-dimensional deformations of the head of the Central Route of the South–North Water Diversion Project in China with TerraSAR-X datasets

As a landmark in China’s hydraulic engineering history, the Central Route of the South–North Water Diversion Project (SNWD-CR) plays a major role in alleviating severe water shortages in Northern China. Existing InSAR monitoring of the SNWD-CR based on one-dimensional viewing geometry and Sentinel-1 imaging is insufficient for a comprehensive assessment of deformation causes. Moreover, the poor geocoding accuracy hampers the previous interpretation of the estimated deformations. Here we carry out comprehensive two-dimensional deformation analyses over the head of the SNWD-CR by integrating the multitemporal PS/DS InSAR and the stress–strain model, where the well-designed topography and geocoded error correction can help to identify the causes of deformation. We apply our strategy to ascending and descending TerraSAR-X meter-resolution datasets acquired from June 2020 to February 2021. Geocoding errors in both ascending and descending orbits are corrected, and the relationship between topography error and horizontal positioning error is discussed. The multi-data fusion results reveal insignificant deformations in the east–west direction except for a makeshift rigid-frame bridge, whereas the vertical deformation field shows two uplifts and a subsidence area in the narrow canal with a maximum rate of 23 mm/y, which are likely to be related to rainfall and water diversion pressure. Furthermore, the combination of the external DEM and topographic residual offers the chance to reconstruct the high-accuracy DEM.

Comparative study of compressive behavior of confined NSC and UHPC/UHPFRC cylinders externally wrapped with CFRP jacket

This study conducted a fundamental investigation on compressive behaviors of carbon fiber-reinforced polymer (CFRP)-confined normal-strength concrete (NSC) and ultra-high performance concrete (UHPC)/ultra-high performance fiber-reinforced concrete (UHPFRC) subjected to concentric axial loading. The mechanical behavior of confined UHPC/UHPFRC, such as the failure mode, stress-strain response, and lateral dilation behavior, was found different from that of confined NSC. Specifically, the passive confining behavior of UHPC/UHPFRC was distinguished from NSC in terms of concrete crack evolution. Diverse cracking propagation patterns resulted in distinct dilation ratios and CFRP efficiency factors. The CFRP confinement could delay the formation of shear cracks, resulting in a linear increasing stage of the first branch in the stress-strain curve of CFRP-confined UHPC/UHPFRC. Moreover, existing stress-strain models available for CFRP-confined UHPC/UHPFRC were profoundly evaluated in this study.

Multi-scale coupling numerical modeling of metallic strip flexible pipe during reel-lay process

Complex plastic deformation and local buckling may occur due to the nonlinear contact between the pipe and drum in the offshore pipeline laying by reel-lay method. In this paper, material performance tests are carried out to obtain the nonlinear stress-strain constitutive models for high density polyethylene (HDPE) material and steel strip. Meanwhile, full-scale tensile tests are also conducted to acquire the tension-strain correlation of metallic strip flexible pipe (MSFP). Then, shell element and solid element are combined to establish an ABAQUS multi-scale finite element model (FEM) for MSFP under the coiled laying condition. The proposed multi-scale FEM consists of three components, i.e. two simplified components and one fine component, which could accurately and efficiently simulate the mechanical properties of flexible pipe under the coiled laying condition. The results indicate that: due to the radial extrusion restriction of spiral steel strips, the Mises stress distribution of inner HDPE layer shows a more uniform spiral strip distribution than outer HDPE layer; the most dangerous condition for MSFP may be when it is just partially wound up on the drum; the effect of friction coefficient on the spiral steel strips seems obviously larger than the effects of traction force and drum diameter.

Size effect on the compressive behavior of BFRP RC circular columns: Experiments and a size-dependent stress-strain model

To investigate the size effect on compressive performance of circular concrete columns reinforced with basalt fiber-reinforced polymer (BFRP) bars and spirals, nine geometrically similar columns were fabricated and tested under concentric compression. The variables tested were cross-sectional diameters (200, 400, and 600 mm) and transverse reinforcement ratios (1.2%, 2.2%, and 3.3%). The results evidently indicated the size effect on the confined strength, corresponding strain and deterioration rate (in the post-peak branch) of concrete core confined by BFRP spirals. Specifically, with the cross-sectional diameter changing from 200 mm to 600 mm, the maximum decreases in the confined strength and corresponding strain were 14.1% and 31.9%, respectively, while the maximum increase in the deterioration rate was 318%. In addition, the size effect on confined strength could be weakened with the increase of transverse reinforcement ratio. Increasing the transverse reinforcement ratio could enhance the load-carrying capacity as well as effectively increase the confinement strength and ductility. Finally, a size-dependent stress–strain model, which considers the size effect of confined strength, corresponding strain and deterioration rate, was developed for evaluating the confined behavior of FRP RC columns.

Compressive behaviour of GFRP-confined geopolymeric recycled aggregate concrete: Effects of RA content, GRAC size and confinement ratio

Substituting geopolymeric recycled aggregate concrete (GRAC) for normal concrete (NC) to fill glass fibre-reinforced polymer (GFRP) tubes and produce green high-performance compression members is a promising construction technology. Although extensive research has been conducted on the performance of GFRP tubes filled with NC in the past decade, gaps in knowledge make it difficult to predict the mechanical behaviour of this new composite member. This paper presents an experimental and analytical study on the progressive failure of GFRP-confined GRAC under compressive loads. A comprehensive investigation was conducted on the effects of the confinement ratio, recycled aggregate (RA) content, and tube size on the compressive behaviour of GFRP-confined GRAC. The test results were compared with those from available studies on confined NC specimens with or without RA. This paper found that GFRP tube confinement had an advantage in alleviating the negative impact of RA on GRAC. The RA replacement ratio and cylindric dimension had no influence on the linear relationship between the confinement ratio and strength enhancement ratio. Predictive models considering the effect of RA content and GRAC size were proposed for the compressive strength and ultimate strain of GFRP-confined GRAC. Finally, a recalibrated stress–strain model was developed to describe the compressive behaviour of GFRP-confined geopolymeric concrete.

Development of high performance geopolymer concrete with waste rubber and recycle steel fiber: A study on compressive behavior, carbon emissions and economical performance

Ultra-high performance concrete (UHPC) has good application prospects with its high strength, toughness and good durability performance. However, the high carbon emissions and high cost of its constituent materials are significant factors that limit its development and promotion. This study explores the development of a low-carbon and low-cost rubber modified high performance geopolymer concrete (R-HPGC) using recycled crumb rubber, recycled steel fibers, and low-carbon geopolymer gel. In this study, the compressive experiments of R-HPGC with different rubber volume replacement ratios (0, 5 %, 20 %, 35 %, and 50 %) were conducted to explore the laws and mechanisms of the effect of different rubber volume replacement ratios on the failure mode, compressive strength, deformation, and elastic modulus of R-HPGC. The compressive stress–strain model of R-HPGC considering the rubber replacement ratio were proposed. Meanwhile, a comprehensive evaluation method based on the carbon emission and cost index of concrete per unit strength is proposed to compare the carbon emissions and economical performance of R-HPGC, UHPC and normal concrete (NC). The results show that the compressive behavior of R-HPGC is determined by the mechanical properties and interactions between the mixed aggregates-geopolymer matrix-recycled steel fibers. At a low rubber replacement ratio (≤5 %/≤35 %), the compressive strength of R-HPGC can still reach the standard of ultra-high/high performance concrete (≥120 MPa/≥55 MPa). R-HPGC has a lower comprehensive cost and carbon emission index compared with conventional UHPC. NC has the lowest comprehensive cost index, but its comprehensive carbon emission index is the highest. It is recommended to use a rubber replacement ratio of ≤5 % for R-HPGC, which provides the best compressive mechanical performance, as well as excellent environmental and economical performance. This study provides a low carbon emission, low cost and high performance concrete that can be designed based on a combination of strength, carbon emission and cost.

Axial compressive behavior of recycled ceramic coarse aggregate concrete-filled steel tubular columns

A series of axial compressive tests were performed on recycled ceramic coarse aggregate concrete (RCCAC) cubes and prisms, as well as 36 recycled ceramic coarse aggregate concrete-filled steel tubular stub columns (RCCAC-FSTs) in the present study. RCCAC failure mechanisms, compressive strength, elastic modulus, and microstructure were studied. In addition to the cross-sectional type, the steel content, the confinement factor, and the replacement ratio of recycled ceramic coarse aggregate (RCCA) were chosen as primary variables to investigate the passive confinement effect of RCCAC-FSTs. Analysis of the typical failure modes, the Load (Nue)-longitudinal strain (εL) curve, the Load (N/Nue)-hoop strain (εh) curve, the ultimate bearing capacity, the ductility, and the effect of RCCA replacement ratio were successively performed. The results suggest that the confinement factor determines the development pattern of the load–strain curves, while the use of RCCA influences the failure mode, the elastic modulus, the ultimate strength, the critical strain, and the ductility of specimens. The critical confinement factor for circular and square specimens was also determined. A stress–strain model of RCCAC restrained by steel tube was established and verified through finite element analysis based on a database of test results presented in the present study and existing research.

Moment–curvature behaviour of RC chimney section under monotonic loading–An experimental study

The latest revision of IS: 4998 (2015 edition) incorporates the limit state method of design and proposes a new stress–strain model for concrete and steel for RC chimneys. Many apparent differences can be noticed between the stress–strain relationships of these two materials when the methodologies of IS: 4998–2015 and other well-established design codes are compared.In order to investigate these differences and to find out the methodology which uses most precision in depicting the stress–strain relationship of these materials, four hollow circular test specimens of typical RC chimneys with openings have been specially designed, fabricated and laboratory tested for bending under monotonically increasing lateral loading. As the results of the cross-section at the bottom of the opening near the base of the chimney are found to be the most critical, the behaviour at especially this section has been emphasized.Test results include strength, crack pattern, failure mechanism; further, the results obtained from this experimental study have been compared in the form of ultimate strength, curvature ductility and energy absorption by plotting moment–curvature relationships using design guidelines given in IS: 4998–2015, CICIND 2011 and ACI: 307–08.

Experimental assessment and compressive constitutive model of rubberized concrete confined by steel tube

To investigate the confining effect and axial compressive behavior of rubberized concrete (RuC) confined by steel tube, axial compression tests were carried out on 12 circular RuC cylinders confined by steel tube. The cylinders considered parameters such as steel tube thicknesses (2 mm, 3 mm, 4 mm) and rubber volume replacement ratios of the fine aggregates (0%, 10%, 20%, and 30%). It was observed that the compressive strength of RuC decreases as the rubber volume replacement ratio increases. However, an increase in steel tube thickness enhances the confining effect of the core RuC, leading to an increase in its compressive strength and the corresponding strain, similar to that of conventional concrete. Moreover, post-peak curves are more likely to exhibit a strengthening part in confined concrete with more rubber content. Furthermore, a model was developed to determine the compressive strength of RuC confined by steel tube. Finally, an axial stress-strain model of steel tube confined RuC was proposed, which was validated against test results.

Uniaxial Monotonic and Cyclic Compressive Stress–Strain Model for Concrete-Filled Thin-Walled Helical Corrugated Steel Tubes

Uniaxial Monotonic and Cyclic Compressive Stress–Strain Model for Concrete-Filled Thin-Walled Helical Corrugated Steel Tubes

A constitutive model of expansive concrete and steel fiber-reinforced expansive concrete under tri-axial compression

Expansive concrete (EC) or steel fiber-reinforced expansive concrete (SF-EC) have been adopted for enhancing the performance of concrete-filled steel tube (CFST) columns, while the investigations on confinement mechanism and theoretical model for EC and SF-EC are limited. This study aims to develop a constitutive model for EC and SF-EC under tri-axial compression. In the first part, the results of tri-axial compression tests on 52 concrete cubes, were summarized and collected to form a database. In the second part, the failure criterions of concrete cubes, and performances of four existing stress–strain models were assessed and discussed using the database. The results of tri-axial compression with equal lateral confining stresses generally complied well with the compressive meridians of Ottosen failure criterion, whereas the Lode angles were around 56°–58° for the true tri-axial compression results. However, the existing models substantially underestimated the axial strains at peak stresses by at least 40%, and thus the predicted stress–strain curves deviated considerably from the test results with much steeper initial ascending slopes. To this end, a modified constitutive model was proposed with Montoya et al.’s model as the base form and the key parameters updated as per the result database. The proposed model had good performances in predicting the peak axial stresses and the corresponding strains (average error at 8% and 19%, respectively), as well as the full axial stress–strain curves.

Workability and mechanical properties of GGBS-RFBP-FA ternary composite geopolymer concrete with recycled aggregates containing recycled fireclay brick aggregates

With urbanization developing, various construction and demolition wastes (CDWs) have emerged, causing environmental and social issues. Green concrete materials, such as recycled aggregates concrete (RAC) and alkali-activated cementitious materials, propose for their environmentally friendly construction. In this study, the ground granulated blast furnace slag (GGBS), recycled fireclay brick powder (RFBP), and fly ash (FA) ternary composite geopolymer concrete with recycled aggregates (GRAC) containing recycled fireclay brick aggregates (RFBA) proposed at first. Then, this study investigated the fresh and hardened properties of this concrete. The experimental variables included the two types of ternary composite geopolymer concrete with recycled fireclay brick aggregates (GRA-RFBAC) mix ratios, five replacement ratios of recycled coarse aggregate, and four replacement ratios of RFBP. The workability and mechanical properties of GRA-RFBAC were studied, respectively. Moreover, the micro-structures and hydration mechanisms of GRA-RFBAC were also studied. The results showed the feasibility of applying RFBP and recycled aggregates containing recycled fireclay brick aggregates (RA-RFBA) in geopolymer concrete, i.e. GRA-RFBAC exhibited good workability and mechanical properties. The addition of RFBP could improve the workability of GRA-RFBAC. GRA-RFBAC with 10% RFBP replacement ratio of was found to have the best mechanical properties. The addition of RA-RFBA has a detrimental effect on both the workability and mechanical properties of the GRA-RFBAC. The stress-strain relationship model of GRA-RFBAC was give and the stress-strain curves of GRA-RFBAC were similar to those of Ordinary Portland cement concrete with recycled aggregates.

Effect of compression casting method on the axial compressive behavior of FRP-confined seawater sea-sand concrete columns

The application of the novel compression casting method is beneficial to improve the compressive strength and durability of concrete. However, the compressed concrete fails rapidly after the peak load and exhibits stronger brittleness than the normal concrete, which could impair the seismic performance of the columns. As one of the passive confining measures, wrapping fiber-reinforced polymer (FRP) could be a practical technique to improve the ductility of such brittle columns. In this regard, this study experimentally investigated the axial compression behavior of both the partially and fully FRP-confined compression-cast seawater sea-sand concrete (SSC) columns. The test results indicated that the compression casting method enhanced the compressive strength but weakened the axial deformation capacity of the unconfined and FRP-confined SSC specimens. The compressive strength of unconfined concrete was improved by 38.5% due to compression casting. The measured average FRP rupture strain of the FRP-confined compression-cast SSC specimens was 6.3% smaller than that of FRP-confined normal SSC specimens due to the sudden appearance of the main oblique cracks, indicating poorer FRP utilization efficiency. Meanwhile, the average ultimate axial strain enhancement ratio of FRP-confined SSC specimens decreased from 12.04 to 7.83 after compression casting. The FRP hoop strain of the fully FRP-wrapped columns distributed more uniformly compared to the partially FRP-wrapped columns as the mean value of FRP efficiency factor increased from 0.807 to 0.928. With increasing FRP strip spacing, the post-peak segment of the stress–strain curve transferred from strain-hardening to strain-softening regardless of the confining stiffness. Finally, several existing stress–strain models were employed to examine their accuracy in anticipating the ultimate conditions of the FRP-confined compression-cast SSC columns.

Infrared radiation constitutive model of sandstone during loading fracture

The significant increase in energy demand will inevitably boost the exploitation of natural resources. The exploitation of resources including coal, oil, geothermal, natural gas, shale gas, and other energy has to be extracted with deep mining to fulfill the industry energy demand. With the increase of mining depth and the utilization of deep rock mass, the problem of high ground stress has become increasingly prominent. During high ground stress conditions, the mechanical behavior of hard rock will change significantly. Constructing a reasonable stress–strain damage constitutive model of hard rock is the basis for the design of a resource mining construction scheme, numerical simulation analysis, more accurate acquisition of rock mechanical characteristics, and evaluation of engineering rock stability. This is very crucial that needs to be addressed in a better way to solve the scientific problems of rock engineering. In this research, the infrared radiation observation experiments of sandstone biaxial under different lateral stresses are carried out. It is found that the infrared radiation energy has a near power function relationship with the effective stress in loading and fracture process. The quantitative characterization method of infrared radiation of the first invariant of stress and the second invariant of deviator stress is established. The cumulative high-temperature point scale factor amplitude is proposed to characterize the plastic volumetric strain of sandstone. Based on the effective stress and plastic strain, the plastic and damage models are established respectively. The three-dimensional plastic damage constitutive model of loaded sandstone based on infrared radiation is constructed. The model has clear input parameters having physical significance, and the compaction stage of sandstone is considered. The stress prediction of sandstone during biaxial loading is realized through the secondary development of a finite element software subroutine. The research results can lay a theoretical foundation for the analysis and evaluation of the mechanical characteristics of hard rock in the process of deep energy exploitation.

The nonlinear energy model and stress–strain model of sandstone

The relationship between strain and elastic energy is simplified by introducing a stress state parameter based on the generalised Hooke’s law. It is assumed that the micro-element strengths satisfy the Weibull distribution and a new model for the non-linear evolution of energy is developed by introducing the concept of rock micro-element strengths. A sensitivity analysis of the model parameters is carried out on this basis. The results show that the model agrees well with the experimental data. The model is close to the deformation and damage laws of the rock and is able to reflect the relationship between the elastic energy and strain of the rock. By comparing with other model curves, the model of this paper is more suitable for the experimental curve. They show that the improved model could better describe the stress–strain relationship of rock. Finally, according to the analysis of the influence of the distribution parameter on the variation pattern of the elastic energy of the rock, the magnitude of the distribution parameter can directly reflect the peak energy of the rock.

Experimental, Numerical, and Analytical Studies of Uniaxial Compressive Behavior of Concrete Confined by Ultra-High-Performance Concrete

This research examines the uniaxial behavior of core concrete, which is confined by a UHPC (ultra-high-performance concrete) shell, through experimental, numerical, and analytical methods. Various configurations, including different UHPC shell shapes, thicknesses, and core concrete compressive strengths, were tested until failure occurred. Results indicate that the UHPC shell altered the failure modes and enhanced the maximum stress and corresponding strain in uniaxial loading. Additionally, in square and rectangular specimens, debonding between the UHPC and NC (normal concrete) interfaces was observed. Furthermore, we constructed numerical models which integrate the concrete damage plasticity model for NC/UHPC and the coupled adhesive-frictional model implemented in cohesive elements. The model accurately reflects the crack and debonding evolution of the tested specimen. Subsequently, an analytical stress-strain model for uniaxial loading was created based on the experimental results. The confining pressure for square/rectangular specimens was determined using Airy’s function. The validity of the analytical model was verified by comparing its predictions with the experimental results.