Crack Theory Research Articles

UHPFRC hidden capitals as an alternative method for increasing punching shear resistance of LWAC flat slabs

Due to outstanding strength properties of contemporary ultra-high performance fiber reinforced concretes (UHPFRC), they can be successfully used to improve the punching shear resistance of flat slabs made from lightweight aggregate concrete (LWAC). However, the relatively high cost of UHPFRC means that the application is usually limited to the support zone or the subsurface layer of the slab.The paper presents the results of experimental investigations on application of the UHPFRC hidden capitals to increase punching shear capacity of LWAC slabs. The study was a continuation of the previous experimental program and included a total of three 200 mm thick slabs with the same longitudinal reinforcement ratio, equal to 1.23%. One was the control specimen made entirely from LWAC, while in the others 130 mm thick capitals from UHPFRC with 2.5% and 5.0% fiber content were cast. The application of hidden capitals allowed to increase the stiffness and reduce deflections of the slabs by about 16 ÷ 20%. The residual strength of UHPFRC was found to be the key feature. In case of the slab with capital from UHPFRC with 2.5% fibre content, shear crack formed at the edge of the column and crossed the capital. However, the contribution of UHPFRC strength allowed to increase the punching shear capacity by 29% with respect to the control specimen. The doubling of fiber content to 5.0% changed the failure mechanism, because the shear cracks formed at the edge of the capital, what was similar to observed in slabs failed outside punching shear reinforced area. This translated into a significant increase in the load capacity by 82% in comparison to the control slab.The performed analysis demonstrated the usefulness of the Critical Shear Crack Theory (CSCT) and the Variable Engagement Model (VEM) for the assessment of the punching shear resistance of LWAC slabs with hidden capitals from UHPFRC. A good agreement of load-rotation response and ratios of theoretical to experimental load equal to 0.87 and 1.16 were obtained. The calculations allowed for correct prediction of the failure mode – punching within or outside the capital.

MODEL OF SHEAR RESISTANCE OF CONCRETE ELEMENTS REINFORCED WITH FRP BARS

Introduction. The problem of shear resistance of reinforced concrete elements without transverse reinforcement remains, as before, one of the most controversial in the theory of concrete structures. A new interest in the problem arose in connection with the use of polymer composite (FRP) bars as longitudinal reinforcement in concrete structures. The models of shear resistance included in the regulatory documents and formulated as proposals for elements reinforced with steel bars and FRP bars are considered. It is shown that the critical shear crack theory (CSCT) can be adopted as a basis for formulating a model of shear resistance of FRP-reinforced elements. However, its provisions cannot be applied directly without appropriate adjustments, in particular, regarding the determination of the width of the opening of a critical crack. Materials and methods. To determine the shear strength of self-stressed concrete elements reinforced with FRP bars, a modified model has been developed. This model, using an iterative procedure, makes it possible to determine a separate contribution to the total shear strength of each of its main components, taking into account the shape of the potential inclined crack, adopted in accordance with the provisions of the Critical Shear Crack Theory (CSCT), as well as the width of the opening of the inclined crack at the level of the longitudinal reinforcement, determined according to the law of "bond-slip" for FRP bars. Results. The reliability of the proposed modified shear resistance model is confirmed by comparing the calculation results with the results of our own experimental data, and with the results of research by various authors (database). Based on the results of a parametric study, a phenomenological shear resistance criterion for flexible elements reinforced with polymer composite bars was proposed, on the basis of which a simplified design model was developed that allows determining the shear resistance of concrete elements reinforced with FRP bars without the need to calculate all components of the shear force. Conclusions. The proposed model of shear resistance of flexible self-stressed elements reinforced with FRP bars reflects the physical essence of the shear phenomenon and is applicable to various cases and loading schemes.

Mechanical analysis of adhesion between wearable electronics and human skin based on crack theory of bi-material interface

In recent years, wearable electronics have been gradually applied in the measurement of human health signals with the development of the technology and the increasing attention to health. The application of the electronic device requires it to be attached to the human skin for an extended period of time. Therefore, it is of great significance to define and judge the comfort of flexible electronic devices. This paper focuses on the adhesion between wearable electronics and human skin based on crack theory of bi-material interface. The comfort of the skin is judged by the magnitude and gradient of the stresses, based on the working principle of human tactile receptors. For the comfort design of wearable electronics, the effects of mechanical and geometric parameters for devices on the skin surface stresses are also discussed. This article provides the theoretical basis for improving the comfort of wearable electronic devices.

Residual punching shear capacity of corroded reinforced concrete slabs

Steel reinforcement corrosion is becoming a critical issue due to the amount of old buildings still in operation with a high probability of substantial corrosion in their reinforcements. The strength and serviceability of corroded reinforced concrete (RC) slab is remarkably impacted by corrosion. Therefore, it is vital to understand more about the punching shear mechanism of slabs subjected to corrosion effects in order to make a good prediction regarding residual capacity. In this paper, critical shear crack theory (CSCT) was further developed to predict the residual punching shear strength of corroded RC slabs, considering the deterioration of material properties induced by corrosion. The effectiveness of modified CSCT was verified by comparison with the available experimental results. In addition, a validated finite element model that considers material deterioration and bond degradation was proposed to verify the accuracy of the proposed model. Finally, a parametric study of 240 cases was conducted to investigate the effect of some important factors on the punching shear behaviour of corroded RC slabs based on modified CSCT. The outcomes demonstrated that the residual punching shear capacity predicted by the proposed model is more accurate than existing design codes. The predicted failure modes also showed fairly good agreement with the experimental results.

Evaluation of the residual carrying capacity of a large-scale model bridge through frequency shifts

Structural systems are often subjected to degradation processes due to different kinds of phenomena like unexpected loadings, ageing of the materials, and fatigue cycles. This is true, especially for bridges, in which their safety evaluation is crucial for planning maintenance activities. This paper discusses the experimental evaluation of the residual carrying capacity from frequency changes due to distributed damage scenarios. For this purpose, in the laboratory of the University of Bologna, an experimental reinforced concrete model bridge was built and loaded. The applied forces produced bending moments causing up to three increasing levels of damage severity, namely early and diffused concrete cracking, and finally rebar yielding. By processing the acceleration signals recorded during the dynamic tests on the model bridge, the main natural frequencies of the bridge were obtained and the remaining bearing capacity was estimated based on the damage state. The opening and closure of cracks during a dynamic excitation produced a biased estimation of natural frequencies related to each damaged condition. The frequency decay predicted by the theory of breathing cracks applied to the performed experiments properly estimated the losses in the carrying capacity.

Finite element modelling of RC slabs strengthened against punching shear with L-CFRP laminates

ABSTRACT Punching shear strengthening of existing reinforced concrete (RC) flat slabs can be required due to increased loads or design/construction defect. One of the more effective punching shear strengthening solutions, which has shown promising results is the use of post-installed L-shaped carbon fibre-reinforced polymer (L-CFRP) laminates bonded into predrilled holes through the slab in specific shear perimeter arrangements around the column. This paper presents an extensive finite element analysis (FEA) into RC slabs strengthened in punching shear using L-CFRP laminates. FEA models were developed using an existing experimental study as the baseline. After successful model calibration, parametric studies were used to explore the influence of critical parameters such as the concrete strength (32, 40 and 60 MPa) and the number of shear perimeters on the resulting punching shear capacity. In total, four RC slabs were modelled including an unstrengthened control specimen and an additional three specimens with different strengthening arrangements. A bond-slip model was introduced between the CFRP and the concrete and its calibration was described in this paper. Simulation results are compared with the experimental results in terms of load–deflection behaviour, FRP strains and crack patterns. The predicted peak loads calculated from the design codes and critical shear crack theory (CSCT) are compared and discussed in conjunction with the experimental and FEA results. The failure mode for the slabs were also compared with design codes and CSCT theory predictions. The study demonstrated the FEA results to have a good agreement with the experimental results in terms of load deflection behaviour, failure mode and L-CFRP strains.

Modelling elastic properties of partially saturated porous rocks with aligned fractures

SUMMARY A simple but rigorous extension to anisotropy of the isotropic theory for partially saturated rocks is developed to model the variations of the P-wave velocities with angle of incidence and water saturation in partially saturated fractured rocks. The theory is developed to match ultrasonic measurements on a synthetic sandstone samples with a regular distribution of aligned, penny-shaped fractures. The velocity anisotropy in the dry fractured sample is well described with a set of standard anisotropic effective medium theory for penny-shaped cracks. The saturation dependence of the velocities is modelled by a combination of four mechanisms (squirt flow, uniform saturation, patchy saturation and full water saturation) and described by four corresponding theoretical models (squirt-flow relaxation model, anisotropic Gassmann–Wood equations, Backus average and anisotropic Gassmann equations). At ultrasonic frequencies, this simple but rigorous combination of poroelastic models can describe angle and saturation dependency of velocities and moduli in a partially saturated fractured and porous rock reasonably well.

A mechanical and simplified model for RC elements subjected to combined shear and axial tension

Very little is known about the shear behavior of elements, in particular those subjected to axial tension. The shear accompanied by tensile forces could cause premature failure of reinforced concrete, which is sudden with minimal warning. Therefore, understanding the shear behavior of reinforced concrete (RC) elements, including those subjected to axial tension, is an ultimate goal of the worldwide research community. In the current study, a new shear mechanical model for RC elements subjected to axial tension is developed, which makes physical sense and explains the behavior. The model is strain-based, inspired by the critical crack theory model (CSCT). In addition, the proposed model extended CSCT (ECSCT) quantifies the effect of axial tension forces on the shear strength in terms of reduction in the compression zone depth and increase in the longitudinal strain. Moreover, the nonlinear trend observed in the literature was implemented using nonlinear multi-variable regression. The ECSCT is validated and compared with available design methods with respect to an extensive database, including 180 elements tested under shear and tension from 18 different research investigations. The ECSCT provided an accurate and physically sound model yet safe to an acceptable extent. Last but not least, a simplified model for the purpose of design is proposed. The simplified model was chosen based on the mechanical model and calibrated using the extensive experimental database. The simplified model provided an accurate and simple model, yet safe to an acceptable extent.

Punching shear strength and deformation for FRP-reinforced concrete slabs without shear reinforcements

While very little is known about the punching shear behavior of Fiber Reinforced Polymer (FRP)-reinforced concrete slabs; thus, very few design codes for this case are available. Most available design codes and guidelines are missing the physical meaning of various aspects. In addition, the critical shear crack theory (CSCT), developed in the '90s for shear and punching shear of concrete elements, has covered a wide range of shear and punching shear problems but did not tackle punching shear of FRP-reinforced concrete slabs. The strength of FRP-reinforced concrete slabs is different from the conventional steel-reinforced concrete slabs in several ways, including but not limited to: (1) having a variable young’s modulus depending on the type of FRP; (2) the flexure strength of FRP-reinforced concrete slabs is different, while the failure occurs due to concrete crushing; and (3) FRP is linear up to failure with no yield plateau. This study aims to develop a mechanical model based on FRP-reinforced concrete slabs' physical punching shear behavior. An extensive experimental database was collected with 189 FRP-reinforced concrete slabs from 37 different studies. A new mechanical model was developed and proposed based on the critical shear crack theory (CSCT). The proposed model captured the behavior accurately and was based on a physical model. The proposed model included the effect of young’s modulus and the different failure modes. It can predict both the strength and rotation of FRP-reinforced concrete slabs under punching shear.

Experimental investigation on punching shear behaviour of RC-(R)UHPFRC composite flat slabs without transverse reinforcement

Strengthening existing reinforced concrete (RC) flat slabs by casting a thin layer of ultra-high performance fibre-reinforced cementitious composite (UHPFRC) over the top surface constitutes an efficient solution for significant durability and flexural capacity enhancements. Previous research has shown that also the punching shear capacity can be substantially increased. However, the existing experimental evidence is still limited and does not allow a systematic evaluation of the influence of the governing parameters.In the present work, eight slabs without transverse reinforcement were tested up to punching shear failure. The following parameters were studied: the contribution of the UHPFRC overlay with and without reinforcement bars, the shape of the column (square or rectangular), the effect of the reinforcement ratio in the existing slab, the eccentricity of the punching force and the material of the strengthening layer (UHPFRC or ordinary RC). The height of the RC substrate and UHPFRC layer thickness were kept constant at 180 mm and 40 mm, respectively.The results confirm the significant contribution of the UHPFRC layer to the punching shear strength. The experimental failure loads are compared to the predictions provided by a composite failure criterion based on the Critical Shear Crack Theory and taking into account the contribution of the UHPFRC layer. Good agreement was obtained with the model being capable of reproducing the effect of all the studied variables.

Thermal destruction of polymeric fibers in the theory of temporary dependence of strength

Objectives. This study mathematically describes the mutual influence of micro- and macrostages of the process of destruction of polymer materials and determines its main parameters and limiting characteristics. In addition, a relationship is established between molecular constants characterizing the structure of a material and those characterizing its macroscopic characteristics of strength. Finally, theoretical representations of the thermokinetics of the process of thermal destruction of polymer fibers from the standpoint of the kinetic thermofluctuation concept are developed, which makes it possible to predict the thermal durability of a sample under thermal loading.Methods. The structural–kinetic thermofluctuation theory was used to describe the initial stages of the fracture process and to derive a generalized formula for the rate of crack growth. The mathematical theory of cracks is used to describe the thermally stressed state of a material in the vicinity of an internal circular crack under mechanical and thermal loadings of the sample.Results. A theoretical formula for the full isotherm of durability in the range of mechanical stresses from safe to critical, as well as a theoretical relationship for the time dependence of the strength of polymer fibers under purely thermal loading in the full range of heat loads from safe to critical and at the stage of nonthermal crack growth, is given. The main parameters and limiting characteristics of durability under thermal loading are also indicated.Conclusions. A generalized structural–kinetic theory of the fracture of polymer fibers under purely thermal action on cracked specimens is presented. The developed theory combines three independent approaches: structural–kinetic (thermofluctuation theory), mechanical, and thermodynamic. The obtained theoretical relations are of practical interest for the development of methods for localization, intensification, and control of the crack growth kinetics.

К 60-летию со дня рождения проф. Юрия Николаевича Радаева

10 февраля 2022 г. исполнилось 60 лет известному ученому в области механики деформируемого твердого тела и прикладной математики, педагогу, организатору науки и высшего образования в России Юрию Николаевичу Радаеву. В статье приведены основные библиографические данные Ю. Н. Радаева, в краткой форме представлены главные научные направления и результаты научной деятельности по фундаментальным проблемам математической теории пластичности, механике растущих тел и рассеянного накопления поврежденности, теории трещин, микрополярной упругости, связанной гиперболической термоупругости и термомеханике, общим математическим вопросам механики сплошных сред, механике сыпучих и гранулированных сред.

Punching Shear Strength Prediction for Reinforced Concrete Flat Slabs without Shear Reinforcement

Failure of flat slabs usually occurs by punching shear mode. Current structural codes provide an experience-based design provision for punching shear strength which is often associated with high bias and variance. This paper investigates the effect of adding a horizontal reinforcement mesh at the top of the slab-column connection zone on punching the shear strength of flat slabs. A new equation considering the effect of adding this mesh was proposed to determine the punching shear strength. The proposed equation is based on the Critical Shear Crack Theory combined with the analysis of results extracted from previous experimental and theoretical studies. Moreover, the equation of load-rotation curves for different steel ratios together with the failure criterion curves were evaluated to get the design points. The investigated parameters were the slab thicknesses and dimensions, concrete strengths, size of the supporting column, and steel ratios. The model was validated using a new set of specimens and the results were also compared with the predictions of different international design codes (ACI318, BS8110, AS3600, and Eurocode 2). Statistical analysis provides that the proposed equation can predict the punching shear strength with a level of high accuracy (Mean Square Error =2.5%, Standard Deviation =0.104, Mean=1.0) and over a wide range of reinforcement ratios and compressive strengths of concrete. Most of the predictions were conservative with an underestimation rate of 12%. Doi: 10.28991/CEJ-2022-08-01-013 Full Text: PDF

Strengthening flat slabs without shear reinforcement against punching shear by concrete overlay

Research in this paper presents a theoretical study of increasing in punching shear capacity of the strengthened flat slab by concrete overlay. The parametric study is based on comparison of three different relevant standards design models and presents results how Eurocode 2 (EN 1992-1-1), Model Code 2010 and draft of second generation of Eurocode 2 (prEN 1992-1-1) take into account strengthening by concrete overlay. A reference specimen is represented by a fragment of a flat slab supported by circular column. Influence of concrete toppings depends on thickness and also on reinforcement ratio. In Eurocode 2 and new generation of Eurocode 2 the increase of punching shear resistance of the slab with concrete topping can be taken into account only by reinforcement ratio and thickness of the slab considering the perfect connection and bond between the original slab and new layer of concrete overlay. Model Code 2010 is based on Critical shear crack theory and the reinforcement ratio in concrete topping was considered in equation of moment of resistance and punching shear resistance is calculated by considering the rotation and deformation of the slab. Estimation of results by parametric study are compared by non-linear model from Atena software.

Application of critical shear crack theory on punching of flat slabs

This article deals with the punching capacity of a flat slab fragment supported by an internal atypically elongated column. Based on the results of this analysis and the application of Critical Shear Crack Theory, the reliability of two design models was determined. The CSCT model is a mechanical model where the shear force transferred by concrete in shear crack can be determined by accounting for the roughness and opening of a critical shear crack. The crack width is proportional to the slab rotation, which was obtained from a nonlinear program Atena and from experimental test and shear capacity was obtained by integrating the shear strength along the control perimeter. The aim of this analysis was to compare the application of CSCT in non-linear analysis and experimental test to point out the significant difference between obtained results, which shows the importance of experimental tests realization. Non-linear analyses provided unsafe results. Contrary the currently used EC2 model provided safe results when reduction of the control perimeter was applied. The best results were obtained in a combination of the CSCT model with measured rotations of the slab specimen.

A comparison of punching shear strengthening of RC flat plates with FRP bars and steel bolts

This study investigated the behavior of carbon fiber-reinforced polymer (CFRP), aramid fiber-reinforced polymer (AFRP) bars and steel bolts as post-installed shear reinforcements for strengthening flat plate structures to evaluate their cost and performance effectiveness via a series of monotonic load tests. Seven interior slab–column connections with a square column including one control specimen and six strengthened specimens with a single-line cruciform shear reinforcement were tested. Two shear reinforcement ratio conditions were examined, which comprised four and seven bars on each side of the column corresponding to 0.75 and 0.5 times the effective slab depth, respectively. The results were compared with the well-established design guidelines, revealing that the shear capacity of the specimens with post-installed shear reinforcement increased to a level where the failure mode changed from punching shear to flexure, resulting in more ductile behavior of the specimens. Additionally, the critical shear crack theory was used to characterize the performance of the specimens; the experimental results agreed well with the theory. The study indicated that FRP materials are competitive compared to the steel material.

How Does In Situ Stress Rotate Within a Fault Zone? Insights From Explicit Modeling of the Frictional, Fractured Rock Mass

AbstractWe quantitatively investigate the spatial stress variations within the fault zone rock mass by explicitly incorporating macroscopic fractures into a 2D multilayer model. Based on elastic crack theory, we first derive a unified constitutive law for frictional fractures, featuring elastic and plastic shear deformation and shear‐induced dilatancy. To honor the varying degrees of damage across fault zones, the multilayer model is composed of varying densities of randomly oriented frictional fractures from layer to layer. Under the boundary conditions specific to fault zones, the global mechanical response of each layer is quantitatively related to the local fracture deformation. We show that the major principal stress always rotates toward a limiting angle of 45° with respect to the fault plane and that the differential stress invariantly decreases with increasing fracture density. Approaching the fault core, the mean stress can either increase or decrease, depending on whether the fault strikes at a high (>45°) or low (<45°) angle to the regional major principal stress. Accumulated damage also results in the decrease and increase of the effective Young's modulus and Poisson's ratio of the fractured rock mass, respectively. Both the fracture properties and pore pressure affect the stress variations by modulating the fracture‐associated deformation and the relative proportion of the elastic and plastic components. Our model illuminates the systematic variations of in situ stresses and effective elastic properties within the damage zone of a mature fault.

Punching shear strength of corroded reinforced concrete slab-column connections

The use of de-icing salts on reinforced concrete (RC) car-park flat slab buildings is known to corrode the reinforcement, which may adversely affect the punching shear strength of the slab-column connections. The consequence of the punching shear failure of slab-column connections can be catastrophic, as the failure of one connection can easily spread to others and eventually leads to the progressive collapse of the flat-slab structure. To study the effects of corrosion of the flexural reinforcement on the punching shear behavior of slab-column connections, twelve full-scale RC slab-column connections were constructed and tested in this study. The experimental program was divided into two stages: 1) accelerated corrosion test; and 2) punching shear test. It was found that the rebar corrosion can change the failure mode of the connection from flexural or shear-flexural failure to punching shear and reduce the punching shear strength significantly. Moreover, the existing design formulas given by ACI 318–19, CSA 23.3–14, Eurocode 2, and BS 8110–97 were found to be unreliable for the prediction of the punching shear strength of corroded slab-column connections. The critical shear crack theory (CSCT) was modified in this work to predict the punching shear strength of the corroded slab-column connection well.

Design of biaxially loaded external slab column connections

The paper investigates the influence of biaxial loading on punching resistance at square and elongated edge columns of flat slabs which is virtually neglected in the literature. In the absence of experimental data, the influence of biaxial loading is determined using nonlinear finite element analysis (NLFEA) with 3D solid elements. The resulting baseline punching resistances are compared with the predictions of various implementations of the Critical Shear Crack Theory (CSCT) including a Joint Shell Punching Model (JSPME) in which punching failure is simulated using nonlinear joint elements inserted between the nodes of nonlinear shell elements located around the punching control perimeter. The failure criterion of the JSPME, which is most suited for structural assessment, implicitly accounts for the effect of biaxial loading unlike the original (classic) and closed form versions of the CSCT. The classic CSCT indirectly accounts for loading eccentricity by reducing the punching control perimeter by a multiple ke which is determined in this paper using shear field analysis. Conversely, the closed form CSCT, which is adopted in the draft for the next generation of Eurocode2 (EC2), enhances the design shear force by a multiple β. The paper uses experimental data to determine an expression for β for edge column connections subject to inwards eccentricity normal to the slab edge. Subsequently, shear field analysis on representative flat slab to edge column connections is used to extend this expression for β to edge column connections subject to biaxial eccentricity. NLFEA simulations with 3D solid elements are used to validate the predictions of the JSPME, the shear field methodology used to determine ke in the classic CSCT and the proposed expression for β in the closed form CSCT. Reasonable agreement is achieved between all these analysis methods. The main advantage of the JSPME over NLFEA with 3D solid elements is its increased computational efficiency which makes it more suitable for the assessment of large structures.

Failure analysis of collapsed parking garage building due to punching

The article deals with failure analysis of collapsed parking garage building due to punching shear failure of the roof slab. Overloading of the roof slab-column connections led to the progressive collapse of the five-story building. The reason of the failure is known however, answer how the structure could withstand such a high level of overloading for 8 months when the ratio of design values of shear force vs. punching capacity βVEd/VRd reached a value of 3.9 provides the article. The design equations for prediction punching capacity, e.g. the EC2 or ACI 318–19 model, are empirical models calibrated using results of the tests carried out on isolated slab specimens. Therefore, they do not allow take into account the favourable effect of membrane forces and redistribution of bending moments in continuous flat slabs. Application of the Critical Shear Crack Theory (CSCT) in combination with non-linear finite element analysis has shown actual punching shear capacity of the system.