Figure 1. Representation of loading surfaces in normalised strain energy release space (taken from Khan and Zahra (2019) ) A schematic showing stress and fracture surfaces with bounding limits and a shaded damaged induced elastic zone. The schematic shows a stress-based failure model with mul... More about this image found in Representation of loading surfaces in normalised strain energy release spac...

Figure 2. ANN architecture for (a) concrete compressive strength, (b) elastic modulus, (c) α, and (d) β A schematic compares four artificial neural network architectures with different input variables, hidden layer sizes, outputs, and dataset sizes. The schematic presents four panels labelle... More about this image found in ANN architecture for (a) concrete compressive strength, (b) elastic modulu...

Figure 3. Definition of normalised distance, d (a) meridian plane (b) π plane (after Abu-Lebdeh and Voyiadjis (1993) ) A schematic shows tensile and compression meridians and a three dimensional stress surface with a stress point, angles, and distance measures. The schematic presents two related representations of a stress surface. The left panel shows the tensile meridian at theta equals 0 degree and the compression meridian at theta equals 60 degrees, plotted in a plane defined by rho on the vertical axis and xi on the horizontal axis. A stress point is marked inside the surface, and the distances delta bar and delta are indicated between the stress point and the bounding surface along the meridian direction. The right panel shows the same stress surface in principal stress space with axes labelled sigma one, sigma two, and sigma three. A stress point is located inside the surface, the Lode angle theta is shown between reference planes separated by 60 degrees, and the distances delta and delta bar are drawn from the stress point to the surface, with the ratio d defined as delta over delta bar. More about this image found in Definition of normalised distance, d (a) meridian plane (b...

Figure 4. Flow chart for programme EPDRAC A flowchart outlines a step-by-step numerical procedure for stress-strain damage analysis under proportional and non-proportional loading. The flowchart shows a computational algorithm that begins with a start and reading input information on materia... More about this image found in Flow chart for programme EPDRAC A flowchart outlines a step-by-step nu...

Figure 5. Comparison of proposed model stress–strain curves with the results published by Xiao et al. (2018) after incorporation of plastic strains at replacement percentages of (a) 0%, (b) 30%, (c) 50%, (d) 70%, and (e) 100% A set of stress-strain curves compares experimental results with E P D and E D models for recycled aggregate concrete from R A C 0 to R A C 100. The image presents five compressive stress versus strain plots labelled a to e for recycled aggregate concrete with increasing replacement levels R A C 0, R A C 30, R A C 50, R A C 70, and R A C 100. In each plot, the vertical axis shows compressive stress in megapascals and the horizontal axis shows strain. Three curves appear in every plot: experimental data, the E D model, and the E P D model. All curves rise steeply to a peak stress between about 40 and 45 megapascals at low strain, then soften with increasing strain. The E P D curves generally follow the experimental response more closely near the peak and along the post peak region, while the E-D curves show faster stress degradation at larger strains. More about this image found in Comparison of proposed model stress–strain curves with the results publishe...

Figure 6. Stress–strain curves for uniaxial compression A set of compressive strength versus strain curves compares experimental results and model predictions for concrete strengths of 27.6, 65, and 120 megapascal. The graph shows compressive strength plotted against strain for three concrete ... More about this image found in Stress–strain curves for uniaxial compression A set of compressive stren...

Figure 7. Comparison of experimental stress–strain curves obtained with the proposed model EPDRAC for w/c = 0.4 at replacement percentages of (a) 0%, (b) 30%, (c) 50%, (d) 70%, and (e) 100% Five stress-strain plots compare experimental results and E P D R A C predictions for compressive behav... More about this image found in Comparison of experimental stress–strain curves obtained with the proposed ...

Figure 8. Comparison of experimental stress–strain curves obtained with the proposed model EPDRAC for w/c = 0.5 at replacement percentages of (a) 0%, (b) 30%, (c) 50%, (d) 70%, and (e) 100% A set of five compressive stress-strain graphs comparing experimental results and E P D R A C model pre... More about this image found in Comparison of experimental stress–strain curves obtained with the proposed ...

Figure 9. Comparison of experimental stress–strain curves obtained with the proposed model EPDRAC for w/c = 0.6 at replacement percentages of (a) 0%, (b) 30%, (c) 50%, (d) 70%, and (e) 100% A set of five compressive stress-strain graphs comparing experimental results with E P D R A C predicti... More about this image found in Comparison of experimental stress–strain curves obtained with the proposed ...

Figure 10. Comparison of Poisson’s ratio obtained experimentally with the proposed model for RAC100% having (a) w/c = 0.4, (b) w/c = 0.5, and (c) w/c = 0.6 A line graph showing Poisson’s ratio versus uniaxial strain, comparing a solid model curve with a dotted experimental curve. The graph plo... More about this image found in Comparison of Poisson’s ratio obtained experimentally with the proposed mod...

Figure 11. Relationship between damage accumulation and concrete compressive strength for the case of concrete with different replacements predicted through the proposed model for (a) w/c = 0.4, (b) w/c = 0.5, and (c) w/c = 0.6 A set of stress-displacement curves showing compressive stress vers... More about this image found in Relationship between damage accumulation and concrete compressive strength ...

Figure 12. Damage accumulation against (RiRi)1/2 for concrete with different replacements predicted through the proposed model for (a) w/c = 0.4, (b) w/c = 0.5, and (c) w/c = 0.6 A graph set showing normalised radius versus square root displacement for R A C mixtures at ratios 0.4, 0.5, and 0.6... More about this image found in Damage accumulation against (RiRi)1/2 for concrete with different replaceme...

Figure 13. Volumetric dilatation capability of the proposed model compared with González-Fonteboa et al. (2011) of concrete under uniaxial compression A graph comparing normalised stress versus volumetric strain for R A C mixtures using Belen and E P D R A C models. The graph shows normalised stress on the vertical axis plotted against volumetric strain multiplied by 10 to the power negative 6 on the horizontal axis. Curves are presented for R A C 0, R A C 20, R A C 50, and R A C 100, each shown for both the Belen model and the E P D R A C model. All curves start near zero stress at small volumetric strain and increase steeply as strain approaches positive values. The E P D R A C curves generally rise more sharply and reach the maximum stress slightly earlier than the corresponding Belen curves, while differences between R A C contents remain relatively small across the plotted range. More about this image found in Volumetric dilatation capability of the proposed model compared with Gonzá...

Figure 14. Proposed EPDRAC model stress–strain curve comparison with results of published data of Ting et al. (2010) for compressive strength of (a) 35, (b) 45, (c) 55, and (d) 65 MPa A graph set comparing compressive stress versus strain for C 35, C 45, C 55, and C 65 using experiment and E P D R A C curves. The graphs show compressive stress in megapascals on the vertical axis plotted against strain on the horizontal axis for four concrete grades labelled C 35, C 45, C 55, and C 65. Each panel compares an experimental curve with an E P D R A C prediction. In all cases, stress increases rapidly from zero to a peak at strains around 0.002 to 0.003, then decreases with further strain. Peak stress rises progressively from about 30 megapascals for C 35 to above 40 megapascals for C 65. The E P D R A C curves closely follow the experimental curves before peak stress and show slightly different post-peak softening behaviour for each grade. More about this image found in Proposed EPDRAC model stress–strain curve comparison with results of publ...

Figure 15. Comparison of biaxial strength envelope of proposed model with published data of Wang et al. (2020) at replacement percentages of (a) 30%, (b) 70%, and (c) 100% A three-panel plot comparing normalised principal stress relationships from Wang et al. and E P D R A C. The image presents three panels labelled a, b, and c showing relationships between normalised principal stresses. In each panel, the horizontal axis shows sigma 2 divided by f c prime, and the vertical axis shows sigma 3 divided by f c prime, both ranging from 0 to about 2. Each plot compares a dotted curve labelled Wang et al. with a solid curve labelled E P D R A C. In all panels, the curves rise from near 1, reach a rounded peak between about 1.4 and 1.8, then loop back toward lower sigma 3 values as sigma 2 increases. The E P D R A C curves closely match the Wang et al. envelopes with small differences near the peak and descending branch. More about this image found in Comparison of biaxial strength envelope of proposed model with published da...

Figure 16. Comparison of biaxial strength interaction curve for 27.6 MPa A plot comparing normalised stress paths predicted by Kupfer et al. and E P D R A C under biaxial compression. The image shows a closed stress path plotted with normalised stresses on both axes, where the horizontal axis ... More about this image found in Comparison of biaxial strength interaction curve for 27.6 MPa A plot com...

Figure 17. Transverse strains of RAC-50 under biaxial compression (a) 0.5:1 and (b) 1:1 Two stress-strain plots compare normalised principal stress responses from reference models and E P D R A C under different strain conditions. The image contains two panels labelled a and b, each showing no... More about this image found in Transverse strains of RAC-50 under biaxial compression (a) 0.5:1 and (b) 1:...

Figure 18. Normalised triaxial strength with stress ratio for RAC30 and RAC50 at σ 3 σ 1 = 0.1 A line chart compares normalised principal stress responses for R A C 30 and R A C 50 from experiments and E P D R A C across stress ratios. The chart shows normalised prin... More about this image found in Normalised triaxial strength with stress ratio for RAC30 and RAC50 at ...