Post-peak Strength Degradation Research Articles

Prediction of post-peak stress-strain behavior for sensitive clays

Unlike typical soils, sensitive clays undergo extensive post-peak strength degradation with increasing strain and finally disintegrate into a remolded liquid state. Realization of post-peak stress-strain behavior of sensitive clay up to large strains is vital in assessing large deformation problems such as landslides and mud flows. The conventional experimental approaches are uncertain about accurately determining the post-peak stress curve up to large strains (>100%) owing to rapidly increasing testing problems at increasing strains. This necessitates the exploration of an alternative scientific approach to predict the complete stress-strain curve for sensitive clays, which is addressed in this paper. Post-peak stress-strain curves of sensitive clays for different sites are obtained by converting remolding index vs. strain energy curves. Using site-specific data from eastern Canada sites, a mathematical expression is proposed to predict the complete stress-strain curve. Subsequently, an equation is developed for predicting remolding energy based on the stress-strain curve. Finally, it is observed that the post-peak stress-strain behavior is highly site-specific and can be mathematically expressed with a combination of exponential and linear strain-softening curves. Overall, the knowledge of the complete stress-strain behavior contributes greatly to the prediction of post-failure movements closer to reality.

Seismic Behavior of Concrete Bridge Piers Reinforced with Steel or GFRP Bars

This paper evaluates the seismic behavior of eight one-third-scale concrete bridge piers reinforced with various configurations of steel or glass fiber–reinforced polymer (GFRP) bars. Each specimen was tested under a constant axial gravity load, combined with reversed quasistatic cyclic lateral loading. The behavior of the piers was assessed and compared in terms of strength, stiffness, deformability, energy dissipation, and damage. The results indicate that well-detailed hybrid configurations with steel longitudinal bars and GFRP spirals offer a ductile seismic response with reduced postpeak strength degradation. The GFRP spirals were effective in confining the concrete core and restraining longitudinal bar buckling. Piers reinforced with GFRP longitudinal and transverse bars exhibit a stable and deformable seismic response with little residual displacement or strength degradation. However, this behavior was accompanied by a reduction in effective stiffness exceeding 40% and approximately half the hysteretic energy dissipation at an equivalent drift level. All piers reinforced with GFRP bars or spirals exceeded lateral drift requirements set by North American codes.

Nonlinear Static Pushover Analysis of Hollow Shear Critical RC Bridge Piers Under Monotonic Loading: A Comparitive Study

Hollow RC bridge piers exhibit several failure modes when subjected to extensive time varying loads during their service lives. Shear failure of hollow RC bridge piers is very critical as it is brittle in nature involving rapid deterioration of strength with increasing widths of the shear cracks and low ductility. Hence this type of failure is not desirable in the earthquake prone areas. Simulation models that can accurately predict the characteristic load deflection curve parameters (including yield load, peak load, ultimate load and corresponding drift, ductility and post peak strength degradation) are very much essential for efficient design of these structures. In the present study, a nonlinear static pushover analysis of three hollow rectangular RC bridge piers (one flexure critical and two shear critical) has been performed under monotonic loading using four different analysis techniques. The first type of simulation model used in the present study is based on the commonly used fiber based nonlinear beam-column elements with simple uniaxial material constitutive relationships, which are very effective in predicting the flexural response of bridge piers. The second type of simulation model used in the present study is also based on simple fiber based nonlinear beam-column elements. However, the constitutive relationships of steel in this model are modified to predict the post-peak strength degradation in shear critical bridge piers. The third type of simulation model is based on two dimensional (2D) CSMM based smeared RC plane stress elements. The fourth type of simulation model is an analytical model based on the sectional analysis method. The load deflection curve properties obtained from all the simulation models have been compared with each other and also with the experimental data. It has been concluded from the present study that all four models are equally efficient in predicting the behaviour of flexure critical bridge pier. However, in the case of shear critical bridge piers, predictions from the 2D CSMM based simulation model are more accurate.

Experimental study on the seismic behavior of RC columns with high axial compression ratios retrofitted by large rupture strain fiber-reinforced polymer

Fiber-reinforced polymer (FRP) composites being utilized to retrofit reinforced concrete (RC) columns has been well documented. However, the axial compression load of the FRP retrofitting RC columns was relatively limited. Aiming to analyze the applicability of FRP retrofitting RC columns with higher axial compression loads, this paper presents an experimental study on the seismic performance of RC columns retrofitted by the Polyethylene Terephthalate (PET) FRP composites. A total of twelve 1/3 scale RC columns were fabricated, including four control specimens and eight PET FRP retrofitting columns with two retrofit schemes. All the columns were tested under combined high axial compression load and cyclic lateral displacement excursions, and the maximum axial compression ratio reaches 1.1. The seismic performance of RC columns retrofitted by PET FRP was analyzed detailedly from the failure mode, shear force and deformation capacity, energy dissipation and ductility. The test results showed that PET FRP retrofitting changed the failure mode of RC columns from brittle to more ductile. The post-peak strength degradation of the columns was more rapid with the increase of axial compression ratio, but the strength degradation of the PET FRP retrofitting columns was more gradual. PET FRP retrofitting significantly improved the ductility and lateral deformation capacity of the columns even under the high axial compression ratio. PET FRP retrofitting can be applied for the RC columns with serous demand of deformation capacity due to the lighter change of shear-loading capacity and stiffness. Contrastively, the improvement of the seismic capacity of the RC columns retrofitted by the laterally wrapped scheme is higher than that of the striped wrapped scheme. Conclusions from this study provide useful references for the seismic retrofitting of RC structures.

Performance of MgO-Mk based M[sbnd]S[sbnd]H concrete column reinforced with steel and BFRP bars under cyclic loads

Magnesia-metakaolin based Magnesium-Silicate-Hydrate (MSH) cement is an emerging class of potentially cleaner binder systems that offers a sustainable alternative to Portland cement. However, as the current state of knowledge on this material is limited to its cement chemistry and basic mechanical properties, there have not been many studies focused on understanding material behavior when used for structural concrete and how structural elements made with such concrete behave under loads. The current study investigates the feasibility of application of this cement to prepare structural concrete and evaluate the structural performance of the reinforced column made with this concrete. In total, seventeen reinforced concrete column specimens were cast, out of which ten were magnesium silicate hydrate (MSH) cement concrete and seven with general-purpose (GP) Portland cement (PC) concrete. The column section was designed as a half-scaled replica of those commonly used in buildings, and the concrete mixes were designed for self-compacting consistency for medium strength. The column testing program, in which the columns were subjected to cyclic lateral loads under and axial loads, was divided into two groups where in the first group the specimens were reinforced with seismic grade steel whereas, those in the second group comprised of either or both longitudinal and transverse reinforcements replaced with basalt fiber variants. Results of the study revealed the behavior of columns made with MSH concrete to be similar to those made with PC concrete. However, the tendency of the MSH to undergo higher deformation under compression resulted in the column to behave as an over reinforced section and at higher ALR the post-peak strength degradation in sectional capacity was more rapid than in the PC concrete.

Behavior of Partially Grouted Concrete Masonry Walls under Quasi-Static Cyclic Lateral Loading.

Eight partially grouted (PG-RM) concrete masonry walls were tested to study the influence of the strength and width of blocks, the wall aspect ratio, the horizontal and vertical reinforcement ratio, and the presence of edge elements (flanges). The results were analyzed in terms of the failure mode, damage progression, shear strength, lateral stiffness degradation, equivalent viscous damping ratio, and displacement ductility. Additionally, the performances of some existing shear expressions were analyzed by comparing the measured and predicted lateral load capacity of the tested walls. Based on the results, a slight increment in the lateral stiffness was achieved when employing stronger blocks, while the shear strength remained constant. Besides, increasing the width of concrete blocks did not have a significant effect on the shear strength nor in the initial tangential stiffness, but it generated a softer post-peak strength degradation. Increasing the wall aspect ratio reduced the brittleness of the response and the shear strength. Reducing the amount of vertical reinforcement lowered the resulting shear strength, although it also slowed down the post-peak resistance degradation. Transversal edge elements provided integrity to the wall response, generated softer resistance degradation, and improved the symmetry of the response, but they did not raise the lateral resistance.

A validated numerical model for predicting the in-plane seismic response of lightly reinforced, low-aspect ratio reinforced concrete shear walls

A finite element model is developed in LS-DYNA to simulate the in-plane cyclic behavior of lightly reinforced, low-aspect ratio reinforced concrete (RC) shear walls. Data from tests of 22 low-aspect ratio RC shear walls in three laboratories are used to validate the numerical model. The design variables in the testing programs included aspect ratio, day-of-test concrete compressive strength, vertical and horizontal web reinforcement ratio, reinforcement ratio in boundary elements, and yield and ultimate strengths of reinforcement, and these are addressed in the numerical model.The finite element predictions and test results, including the force–displacement relationships and damage to the RC shear walls, are presented and contrasted. Numerical methods are proposed to model the effect of early stage cracking on the initial stiffness of RC walls and to capture post-peak strength degradation. The numerical simulations are in good agreement with the measured responses. The validated LS-DYNA model is used in a parametric study to investigate the effects of wall aspect ratio, reinforcement ratios in web and boundary elements, and compressive axial load on the monotonic response of RC walls. The accuracy of four equations used to predict the peak shear strength of low-aspect ratio walls is assessed using results of the numerical analyses.

Determination of confinement and plastic strain dependent post-peak strength of intact rocks

The post-peak strength behavior of rocks is important for stability analysis of underground excavations. This paper studies the confinement and plastic strain dependent post-peak strength of intact rocks. First, the post-peak behavior of rocks is studied by conducting triaxial compression tests on a coarse marble. The post-peak strengths of the rock under different confining pressures and plastic strains are obtained using the recorded stress–strain curves. A strength degradation index is then proposed to represent the post-peak strength degradation, and a negative exponential function, which includes a shape parameter n, is used to describe the relation between the strength degradation index and the confining pressure. Parameter n is plastic strain dependent, which decreases with the increase of plastic strain. The proposed strength degradation model can well capture the post-peak strength envelopes of the coarse marble under different plastic strains. Finally, two sets of triaxial compression test data from previous studies are used to further verify the strength degradation model. The peak and post-peak strength behaviors of two marbles are well represented using the proposed model. The approach proposed in this study also provides a simple yet useful method for determining the realistic residual strength of intact rocks.

Constitutive model selection for unreinforced masonry cross sections based on best-fit analytical moment–curvature diagrams

A significant number of macroscopic constitutive models is available to simulate the behaviour of unreinforced masonry (URM) in compression, but they produce different predictions of sectional response to eccentric compressive loading. In this paper, nonlinear moment–curvature analysis of rectangular URM cross sections is presented to explore the influence of alternative constitutive models and ultimate limit state assumptions in terms of post-peak strength degradation and strain ductility. Theoretical moment–curvature diagrams are quantitatively compared to experimental data at multiple levels of load eccentricity through goodness-of-fit measures. Different constitutive models are found to produce a good simulation of experimental moment–curvature behaviour, depending on whether experimental data are disaggregated in terms of masonry type or not. Moment–curvature diagrams are derived by keeping constant either the magnitude or the eccentricity of axial load. Finally, the effects of tensile properties and model error of theoretical moment–curvature diagrams are assessed.

Tests on Effects of Loading Rate on Modulus and Strength of Sandstone

For studying on the effects of loading rate on modulus and strength of sandstone, uniaxial compression experiment of the samples, from Balikun mine, was performed at different loading rates. The influence of loading rate on average modulus, uniaxial compressive strength and post-peak strength degradation angle was analyzed, and the results indicate that:: The average modulus of sandstone samples increases with loading rate increasing; the both almost obey linear relationship. The peak strength of sandstone grows with the increase of loading rate; there is an approximately exponential relationship between the two. With loading rate increasing, the post-peak strength degradation angle decreases; the relationship between the both is approximately exponential.

Experimental Study of Steel Frames with Infill Prefabricated Reinforce-Concrete Shear Walls

To realize the industrialized lateral resistant system in steel structure, a low cyclic loading tests is carried out for steel frames with infill prefabricated reinforce-concrete shear walls (solid wall). The crack developed in infill walls and deformation performances of specimen are investigated. And the force transfer mechanism, failure mode, hysteretic behavior, stiffness degradation deformation and ductility and energy dissipation of composite structure are analyzed too. Test results show that the concrete crushing in infill wall is the main failure paten and the failure mode is ductile failure. Within the whole loading period, low cyclic fatigue of shear connectors (U sharp bars) doesn’t occur. The performance of the specimens including post peak strength degradation, ductility behaviors and energy dissipation, are significantly improved. In the whole test the steel and concrete components work integrally. And the specimen has good seismic performances and can be widely used in seismic areas.

Cyclic behavior of partially-restrained steel frame with RC infill walls

In order to investigate the behavior of partially-restrained steel frame with RC infill wall (PSRCW), two specimens with one-third scale, one-bay, and two-story were performed under reversed cyclic lateral load, where one specimen was with concealed vertical slits in the infill walls and another specimen with solid infill walls. Test results showed that both specimens obtained enough lateral stiffness for controlling drift and yielded enough strength appropriate for resisting lateral load. PSRCW with solid infill walls exhibited moderate ductility capacity and energy dissipation due to the degradation of post-peak strength. PSRCW with concealed vertical slits exhibited much larger ductility, deformability, and energy dissipation capacity than the other one. Once concealed vertical slits were crushed, infill walls behaved as a series of flexural columns provided fairly ductile response and stable cyclic performance. PSRCW with concealed vertical slits can improve post-peak strength degradation considerably. In addition, damaged PSRCW structure subjected to earthquake is easy to be repaired, through knocking off the heavy crushed infill walls and recasting concrete infill walls. This is another advantage of this composite structure.

Diagonal shear behaviour of unreinforced masonry wallettes strengthened using twisted steel bars

The in-plane shear behaviour of URM wallettes strengthened using near surface mounted high strength twisted stainless steel reinforcement (TSNSM) was investigated and in particular, the effectiveness of the reinforcing schemes to restrain the diagonal cracking failure mode was studied. A total of 17 URM wallettes, each being 1.2 m × 1.2 m in size, were structurally tested in induced diagonal compression. Of these, 3 wallettes were tested as-built and 14 wallettes were tested after being strengthened using different patterns of TSNSM bars. Several parameters pertaining to the in-plane shear behaviour of strengthened URM walls were investigated, including failure modes, shear strength, maximum drift, pseudo-ductility, and shear modulus. It was inferred from the results that as-built tested wallettes exhibited sudden post-peak strength degradation and failed along a stepped diagonal joint crack, whilst strengthened wallettes failed along distributed diagonal cracks in a more ductile fashion and exhibited a shear strength increment ranging from 114% to 189%.

Cyclic behavior of steel frame structures with composite reinforced concrete infill walls and partially-restrained connections

This paper presents an experimental study of the cyclic behavior of a composite structural system consisting of partially-restrained (PR) steel frames with reinforced concrete infill walls. The composite interaction is achieved through the use of the headed stud connectors along the steel frame–infill interfaces so that the two main components of the system share in the resistance of lateral shear and overturning moment. Having the relatively light steel frame constructed using PR connections maximizes the economy of the system, while still ensuring system integrity in the post-peak range of deformation. The one-bay, two-story test specimen was built at one-third scale. The study shows that this system has the potential to offer strength appropriate for resisting the forces from earthquakes and stiffness adequate for controlling drift for low- to moderate-rise buildings located in earthquake-prone regions. Redundancy is also exhibited in this system through alternate load paths occurring at different levels of loading, including shear stud–infill interaction, steel frame–infill strut interaction, and deformation of the steel frame. Improvement is needed for reducing the post-peak strength degradation observed in the present study.