Nonlinear analysis method of concrete structures under cyclic loading based on the generalized secant modulus

A smeared crack model to represent cyclic concrete behavior is presented in this work. The model is based on analytical and experimental studies from the literature and proposes a numerical approach using a new concept, the generalized secant modulus. The monotonic formulation is described, followed by the changes to include the cyclic response, and the stress-strain laws to reproduce the hysteresis. Simulations adopting the proposed model were compared with experimental tests of cyclic tension and compression available in the literature, resulting in consistent load cycles. Three-point bending was simulated to display the structural response under non-elementary load. Finally, a reinforced concrete beam was studied to evaluate the model performance under usual loadings. The results show the model capacity to reproduce cyclic analyses and its potential to be extended to general loadings.

Residual Stress-Strain Relationship of Scoria Aggregate Concrete with the Addition of PP Fiber after Fire Exposure

Scoria aggregate concrete (SAC) as new green material has been gradually used in some construction projects for its lightweight and high strength, which can reduce the environmental impact of construction materials. In this paper, the residual mechanical properties and intact compressive stress-strain relationships of polypropylene (PP) fiber-reinforced Scoria aggregate concrete after high-temperature exposure at 20, 200, 400, 600, and 800 °C were investigated. The failure modes of PP fiber-reinforced Scoria aggregate concrete specimens and the effect of high temperatures on the peak stress, secant modulus, and peak strain were obtained. The results showed that the residual compressive strength of heated concrete is significantly reduced when the temperature exceeds 400 °C. The residual strength and residual secant modulus of PP fiber-reinforced Scoria aggregate concrete are significantly higher than those of ordinary concrete. The Scoria aggregate concrete specimens with PP fibers exhibited fewer surface cracks and fewer edge bursts under high temperatures. The residual stress-strain equation of the Scoria aggregate concrete was established by regression analysis, which agreed well with the experimental results.

Influence of Dispersed Reinforcement on Mechanical Properties of Stabilized Soil

Stabilized soils are commonly used as part of pavement construction in highway engineering. The everyday use of this material makes it necessary to classify it. One of the basic methods of determining the mechanical properties of a material is the Unconfined Compressive Strength (UCS) test, from which the material elasticity can be determined. The scope of the research included the design and making of soil mixtures stabilized with polypropylene fibers modified cement. This paper presents the effect of the amount of dispersed reinforcement on the maximum compressive strength, the secant modulus at half the ultimate stress (), the secant modulus at the ultimate stress (), and the tangent modulus (). The materials chapter characterizes the soil, cement, and dispersed reinforcement used. The test methods section describes the tests performed and the procedure for interpreting the results. The results section describes the relationship between elastic modulus and compressive strength. The discussion section compares the obtained results with the works of other authors. The work is concluded with a summary containing the most important conclusions resulting from the work.

Consolidated drained (CID) behavior of fibre reinforced cemented Toyoura sand in triaxial loading conditions

The effects of fibre (0–3 %) and cement (0–3 %) additives, on Toyoura sand were examined under consolidated drained compression and extension loading conditions. All samples were prepared to a target dry density value (e.g., $${\rho }_{d}$$ ρ d = 1.489 g/cm3) of Toyoura sand using under-compaction moist tamping technique. In compression, the unreinforced specimens exhibited a behavior of medium dense sand and reached a peak deviator stress (qp) at approximately 4 % axial strain ($${\epsilon }_{a}$$ ϵ a ) for the varying mean effective stresses, pʹ (i.e. 50–400 kPa). The peak drained strength increases in fibre reinforced cemented specimens were found to be up to 132 % (lower effective stresses) and 243 % (higher effective stresses), while, the drained strength increases at critical state for the fibre reinforced cemented specimens were found to be up to 105 % (lower effective stresses) and 245 % (higher effective stresses). Overall, the fibre and cement additives increased the stiffness, peak and strength at critical state of pure Toyoura sand but were found to be least effective in extension loading. Moreover, the stress ratio, peak and critical state stress ratios increase with the addition of fibres and cement. The secant modulus shows limited increases for the fibre reinforced specimens. However, a significant improvement in the secant modulus is observed for the fibre reinforced cemented specimens. For both unreinforced and reinforced specimens there is a decrease in volumetric strain with greater effective stresses or in other words, the rate of dilation decreases with increases in effective stresses. The fibre and cement additives also increased the strength parameters (frictional angle, cohesion), dilatancy angle, slope of the critical state line, and decreased the state parameter of pure Toyoura sand.

Load-Deflection Behavior of Over- and Under-Reinforced Concrete Beams with Hybrid FRP-Steel Reinforcements

The present study pertains to the load-deflection behavior and cracking moments of concrete beams with hybrid FRP-steel reinforcement. Under and over-reinforced hybrid beams were tested for failure along with reference beams with only steel or FRP reinforcement. The first-cracking moments of the beams were estimated analytically by using different uncracked moments of the inertia and modulus of rupture definitions. The uncracked moment of inertia definitions include the gross and uncracked transformed moments. The adopted modulus definitions are comprised of the experimental values from tests on prisms and the analytical values from the equations in different concrete codes. Furthermore, analytical methods were developed for estimating the deflections of concrete beams with hybrid FRP-steel or only FRP reinforcement. Two different types of elastic moduli, namely the secant modulus corresponding to the extreme compression fiber strain and the ACI 318M-19 modulus, were used in deflection calculations. Closer estimates were obtained by using the secant modulus, particularly in hybrid-reinforced beams. In the post-yielding region of the steel tension reinforcement, the deflection estimates were established to lay in closer proximity to the experimental curve when obtained by adding up the deflection increments instead of directly calculating the total deflections from the elastic curve equation. Accurate estimation of the cracking moment was found to be vital for the close prediction of deflections.

Mechanical Behavior of Frozen Porous Sandstone under Uniaxial Compression

The influence of low temperature on longitudinal wave velocity, uniaxial compression strength, tensile strength, peak strain, secant modulus, and acoustic emission characteristics of yellow sandstones was studied. The results show that the secant modulus increases with decreasing temperature when the axial strain is less than 0.6%, and a contrary influence performs for the subsequent stage due to the fracture of the pore ice. With the decrease in temperature, the uniaxial compression strength first increases and then remains at a relatively constant value of 34.44 MPa at about -40°C while the temperature ranges from -40°C to -70°C. The tensile strength shows an approximate linear increment as the temperature. The peak strain gradually increases with temperature in a three-stage piecewise linear form, and the increasing rate gradually decreases with the decreasing temperature. The phase transformation from liquid water at a temperature of 20°C to solid ice at a temperature of -3°C significantly increases the longitudinal wave velocity from 1.55 km/s to 3.36 km/s. When the temperature is lower than -10°C, the longitudinal wave velocity approximately increases linearly at a rate of 2.67 × 10 − 3 km / s · ° C − 1 with decreasing temperature.

Influence of water saturation on the strength characteristics and deformation behavior of hardened cement paste backfill

In this study, a uniaxial compression experimental was conducted to examine the mechanical properties of hardened cemented paste backfill (CPB) with different water saturations (0.18%, 4.98%, 9.30%, 21.6%, 32.8%, and 100%). The experimental results demonstrated that water saturation loosened the overall structure of the CPB, which led to the deterioration of its mechanical properties. As the water saturation increased, the uniaxial compressive strength (UCS), residual strength, strength difference, deformation modulus, secant modulus, E50 (the secant modulus at 50% of the UCS), peak strain, and elastic strain decreased, while the plastic strain ratio increased. The UCS, E50, and peak strain demonstrated exponential function relationships with the water saturation. After the peak point, when the water saturation was less than 20%, the strength of the CPB decreased rapidly, and when the water saturation was greater than 30%, the strength decreased slowly. Lastly, the plastic strain, the strain at 50% of the UCS, and the strain at the maximum secant modulus conformed to the normal distribution, and the water saturation had a minimal impact on these three strains. The fractal dimension, D, of the cracks in the CPB increased exponentially with increasing water saturation and demonstrated a negative linear correlation with the UCS.

Optimizing modified triaxial testing for small strain zone using local displacement transducers and bender element for cement-treated soft soil

The settlement behavior is a common problem on the railway structure that can be optimized by applying cement-treated soil as ground restoration. However, the application of a high cement mixing content needs a proper estimation that can be achieved by adjusting the element testing. The strain measurement devices can estimate the deformation characteristics, such as secant modulus, Poisson ratio, and shear modulus that can describe the settlement behavior and stiffness of cement-treated soil. This research is focused on a static analysis of triaxial consolidated undrained (CU¯) testing that is improved by the axial and radial local displacement transducer (LDT) and bender element to increase the accuracy of measurement results. Furthermore, the secant modulus and shear modulus is more accurate when the combination of radial and axial LDT is used due to a small strain range. Lastly, the shear modulus measurement is improved by using a filler in the cement-treated soil for the bender element test. To conclude, this system of testing for the static condition can be utilized for the dynamic condition, because the measurement shows a reliable result for a small strain range which is the parameter of the dynamics condition.

DIFFERENTIAL EQUATIONS OF CONTINUUM EQUILIBRIUM FOR A PLANE STRAIN IN CYLINDRICAL COORDINATES AT BILINEAR APPROXIMATION OF CLOSING EQUATIONS

Problems of the formulation of differential equations of equilibrium in terms of displacements for a plane strain of continuous media at bilinear approximation of closing equations are considered leaving out of account geometric nonlinearity in the cylindrical coordinate system. Based on the assumption that the curves of volumetric and shear strain are independent from each other, six main cases of physical dependencies are considered, which are the functions of the relative position of break points on the bilinear curves of the volumetric and shear strain. Obtaining of bilinear physical dependencies is based on the calculation of secant moduli of the volumetric and shear strain. On the first line of the curves, secant moduli are constant for both volumetric and shear strain, while on the second line, the secant modulus of the volumetric strain is a function of the volumetric strain, and the secant modulus of the shear strain is a function of the shear strain intensity. Putting the corresponding bilinear physical equations into differential equations of continuum equilibrium, which disregard geometrical nonlinearity, the resulting differential equations of equilibrium are obtained in terms of displacements for a one-dimensional plane strain of continuum in the cylindrical coordinate system. These equations can be used when determining stress-strain state of continuous media under one-dimensional plane strains with no regard for geometrical nonlinearity, and whose physical relations are approximated by bilinear functions.

Tensile mechanical properties of fly ash concrete at early age for thermal stress analysis

The present study investigates tensile properties of concrete with and without fly ash at early age, such as tensile Young’s modulus, strength and creep. Some Young’s modulus of fly ash concrete for thermal crack analysis was compared with the tensile Young’s modulus, secant modulus, initial tangent modulus and linear modulus obtained from the direct tension test and compression test. The tensile creep test was also performed to obtain the specific creep behavior considering decrease in elastic strain due to stiffness development at early age during creep test. The results show that the Young’s modulus for crack evaluation can be obtained from the compression test based on the stress range less than the splitting tensile strength, while the compressive secant modulus was smaller than the tensile Young’s modulus. The decrease of the elastic strain at early age contributes more to the evaluation of the tensile creep than the use of the fly ash mixing.