Crack Theory Research Articles

Punching failure and analytical model for rectangular flat slabs with equal flexural capacities in orthogonal directions

Despite the practical use of rectangular flat slabs with equal flexural capacities in orthogonal directions, their punching behavior has not been addressed. In this paper, the mechanical behavior of such slabs under varying tensile reinforcement ratios and plan dimensions has been investigated, using nonlinear finite element analysis in ABAQUS. Initially, the numerical model of the interior slab-column connection under static vertical loads was developed and thoroughly verified using 20 symmetrical and 9 asymmetrical specimens, covering wide variations in various parameters. Subsequently, parametric studies were conducted on rectangular slabs with equal flexural capacities in both directions, utilizing 54 simulations. The results indicated that the slab aspect ratio strongly affected the load-rotation curves, tensile reinforcement stress, cracking patterns, and shear forces in both directions, as well as their symmetry, despite being designed with equal flexural capacities in orthogonal directions. A novel approach, derived from the critical shear crack theory (CSCT), was developed for this slab type and then compared with existing models. It is noted that the ACI code cannot accurately predict the punching capacity. Although the EN1992–1-1 (2023), MC2010, and CSCT models accurately predict punching capacity, especially when the MC2010 and CSCT models account for two directional rotations, they lack in predicting deformation capacity. However, the proposed model offers accurate predictions for punching and deformation capacities. Its innovations include refining the load-rotation equation, validating the CSCT failure criterion, and quantifying the non-uniform shear force between orthogonal directions.

Optimized Machine Learning Algorithms for Predicting the Punching Shear Resistance of Flat Slabs with Transverse Reinforcement

In the calculation of reinforced concrete (RC) flat slabs with transverse reinforcement, punching shear resistance is one of the most critical factors. It is true that design provisions may be implemented, but they often result in significant biases and deviations from expectations. This study aims to present an optimized machine learning (ML) algorithm for estimating the punching shear resistance. Four machine learning (ML) algorithms (SVR, DT, RF, and XGBoost) with Bayesian optimization (BO) are presented in this paper to provide accurate predictions for flat slabs. The adoptability and optimization of the models are achieved through the analysis of a database of 337 test specimens with nine design parameters. Machine learning (ML) techniques are used to estimate punching shear resistance, which is compared with design provisions and equations relating to critical shear crack theory (CSCT). According to this study, Bayesian optimization is still capable of improving the performance of conventional machine learning algorithms, while the XGBoost-based model offers advanced capabilities. Predictions based on BO-XGBoost are in good agreement with actual values (MAE, RMSE, and R2 are 0.09 MN, 0.14 MN, and 0.92, respectively) in test set. Following a detailed explanation using Shapley additive explanation (SHAP), a high-performance ML approach is used to investigate the predictive results. With the proposed optimized algorithms, it is possible to determine the punching shear resistance of flat slabs with transverse reinforcement during the preliminary stages of the construction.

Flexural performance and crack width prediction of steel-UHTCC composite bridge decks with wet joints

Composite bridge deck (CBD) structure has been widely used in recent decades, particularly in long-span bridges. The application of ultra-high toughness cementitious composite (UHTCC) in composite bridge deck (CBD) structures has garnered attention due to its exceptional resistance to tensile cracking and strain hardening. However, their widespread adoption necessitates a thorough understanding of crack resistance, especially in the presence of wet joints between cast regions. This study investigates the flexural performance and crack width prediction method of steel-UHTCC/concrete CBDs with wet joints using a combined experimental and theoretical approach. Six specimens with UHTCC wet joints and either UHTCC or concrete precast layers were designed and tested under hogging moment. The analysis focused on failure modes, load-deflection responses, and crack development while considering the wet joints. All specimens exhibited interfacial slip between the UHTCC/concrete layer and the steel beam. A novel theoretical model was developed to predict crack width in steel-UHTCC/concrete CBDs with wet joints. This model incorporates established crack theories for fiber-reinforced concrete while explicitly accounting for the strain-hardening behavior of UHTCC. Furthermore, this model provides a detailed bending analysis of steel-UHTCC CBDs considering the interface slip phenomenon, to derive various mechanical parameters for crack width prediction.

A deformability-based mechanical model for predicting shear strength of FRP-strengthened RC beams failed in concrete cover separation

Concrete cover separation (CCS) is frequently happened prior to the yielding of steel stirrups in FRP-strengthened RC beams. However, the debonding mechanism and criterion have not been fully understood. In this study, the typical crack types associated with CCS are comprehensively summarized and investigated in terms of profiles and kinematics of crack. The dowel action and dowelling cracks are proved to be the dominant factors causing CCS. Based on the cracking features, the simplified local debonding strength and average shear strength of fracture interface, which constitutes the contribution of concrete to shear capacity of strengthened RC beams, are analytically derived and verified against the available experiments and code provisions. Through regression analysis of 179 collected shear tests, a formulation based on the Critical Shear Crack Theory (CSCT) is presented to assess the deformability of strengthened RC beams governed by CCS. The commonly overlooked actual stress level in steel stirrups is considered as a function of the rotation capacity of beams and assessed based on the Modified Compression Field Theory (MCFT). Validation of this analytical approach, involving comparison against the empirical models and experimental results from 107 specimens, confirms its superior effectiveness and consistency in predicting CCS and shear strength.

Investigating the impact of corrosion on behavior and failure modes of reinforced concrete slabs: An experimental and analytical study

Corrosion of steel reinforcement significantly reduces the load-carrying capacity of reinforced concrete (RC) flat slabs, making them more vulnerable to punching shear failure. This type of failure can lead to sudden and catastrophic collapse of the structure. Despite its critical implications, research on this topic remains limited, and a mechanical model to estimate the load-displacement behavior of RC flat slabs with corroded reinforcements is currently lacking. In this paper, experimental work on corroded RC slabs under punching shear loading was conducted. To investigate the impact of corrosion on the structural behavior of reinforced concrete (RC) flat slabs, eight specimens, including both corroded and uncorroded controls, were subjected to load testing. The study focused on key performance indicators including punching shear strength, stiffness, crack patterns, failure modes, and energy dissipation capacity. Additionally, an analytical study based on the newly developed Critical Shear Crack Theory (CSCT) was conducted to understand the behavior of corroded RC slabs. Experimental results indicated a significant reduction in the punching shear strength of corroded slabs. Moreover, as corrosion progressed, a notable shift in failure mode from punching shear to flexural failure was observed. The proposed CSCT model demonstrated good agreement between the experimentally obtained and analytically predicted load-displacement curves.

Detection of a cracked and fluid-filled main Himalayan thrust (MHT) and its implications toward the genesis of earthquakes in the Uttarakhand Himalaya

The present study looks into the significant role of metamorphic and aqueous fluids in the mid-crustal Main Himalayan Thrust (MHT) in triggering strong to moderate earthquakes in the Kumaon-Garhwal Himalayas. Using seismic velocity tomograms, crack density (ε) and saturation rates (ξ) have been modelled using the crack theory. All three earthquakes in Uttarakhand with Mw ≥ 6.5 (viz., 1803 Mw7.8 Garhwal, 1991 Mw6.8 Uttrakashi and 1999 Mw6.5 Chamoli earthquakes) occurred within the MHT, which is depicted as a shallow north-dipping layer with low velocity. Our models show that these earthquakes occurred between 10 and 20 km depths where ε (∼0.011–0.012), ξ (∼0.386–0.392), and Vp/Vs (∼1.74–1.90) are all relatively high, indicating a greater possibility of aqueous/metamorphic fluids within the MHT than in the surrounding area. These fluids are suspected to be the trigger for earthquakes in the Uttarakhand Himalaya. As we drill deeper into the crust, we find that ‘ε’ decreases as a result of crack closure (≤0.011), while ‘ξ’ is predicted to increase (∼0.3–0.6) as a result of the presence of more wet and saturated cracks caused by the presence of partial melts (higher Vp/Vs: 1.74–1.92). Our modelling further verifies that the earthquakes in the Uttarakhand Himalaya are primarily driven by the existence of a highly conductive and weakened MHT with a greater concentration of metamorphic/aqueous fluid-filled cracks at depths ranging from 10 to 20 km. The ramifications of our research could significantly impact the earthquake hazard and risk in the Uttarakhand Himalayas.

Punching shear tests and design of UHTCC-enhanced RC slab–column joints with shear reinforcements

Reinforced concrete (RC) flat-slab structures may experience progressive collapse, usually caused by the punching shear failure of slab–column joints. Existing research has shown that the use of shear reinforcements or ultra-high toughness cementitious composites (UHTCCs) in slab–column joints is efficient in improving their punching shear performance. In this study, shear reinforcement was introduced into UHTCC-enhanced RC slab–column joints. Specimens of UHTCC-enhanced slab–column joints were tested considering the effect of shear reinforcements. The cracking development process, bearing capacity and ductility were analysed. Yield line theory and critical shear crack theory were adopted to predict flexural and punching shear capacities, respectively. Finally, the failure patterns of the specimens were distinguished by comparing the predicted punching shear and flexural capacities, taking ductility coefficients into account. The theoretical and test results show the effect of shear reinforcement on the behaviour of UHTCC-enhanced joints. Significant improvements in the bearing capacity and ductility of the joints was achieved by applying shear reinforcement. The failure pattern of the joint varied from premature punching shear failure to flexural-triggered punching shear failure with the application of UHTCC, and this transformation was more pronounced with shear reinforcement applied into the UHTCC-enhanced joint.

Punching shear tests in flat slabs supported on re-entrant corner columns

The punching strength and deformation capacity of slab-column connections is governing for design at ultimate limit state of flat slabs. This phenomenon has been investigated since decades with experimental programmes in an effort to derive empirical or mechanical design approaches. Such efforts, due to the complexity of the phenomena, have mostly been addressed to axisymmetric inner slab-column connections, which correspond to the simplest academic case and are not directly covering a large variety of practical situations. Although some tests are also available for other configurations, such as edge or corner connections, no experimental evidence is found on relevant cases for practice such as re-entrant corner columns. The lack of experimental data in this latter case raises questions on the design of such connections, as extrapolating results from other cases is not a simple task due to the complexity of the phenomena implied (such as redistributions in the shear field and moment transfer between slab and column). In order to advance the knowledge on the response of re-entrant connections and to provide a sound design approach for them, this paper presents the results of an investigation specifically addressed at this case. To that aim, seven specimens were tested under different conditions, varying the load eccentricity, flexural reinforcement and shear reinforcement arrangement at the edges. The tests were instrumented with refined measurements, allowing to understand in a detailed manner the response of the slabs during testing in the shear-critical region. The experimental results are later compared to current design codes, leading to a number of conclusions with practical relevance. Finally, on the basis of the knowledge acquired from the tests, a mechanical approach is proposed based on the Critical Shear Crack Theory to assess the punching response. This approach is shown to lead to accurate and reliable predictions of the punching strength, improving those of current design codes.

Complexity of crack front geometry enhances toughness of brittle solids

Brittle solids typically fail by growth and propagation of a crack from a surface flaw. This process is modelled using linear elastic fracture mechanics, which parameterizes the toughness of a material by the critical stress intensity factor, or the prefactor of the singular stress field. This widely used theory applies for cracks that are planar, but cracks typically are not planar, and instead are geometrically complex, violating core tenets of linear elastic fracture mechanics. Here we characterize the crack tip kinematics of complex crack fronts in three dimensions using optical microscopy of several transparent, brittle materials, including hydrogels of four different chemistries and an elastomer. We find that the critical strain energy required to drive the crack is directly proportional to the geodesic length of the crack, which makes the sample effectively tougher. The connection between crack front geometry and toughness has repercussions for the theoretical modelling of three-dimensional cracks, from engineering testing of materials to ab-initio development of novel materials, and highlights an important gap in the current theory for three-dimensional cracks.

Limits for the Punching Shear Capacity of the Flat Slabs Reinforced with Transverse Reinforcement

One of the most effective and common ways of an increasing the punching shear capacity of the flat slabs is using of shear reinforcement. An important limit during the design is the determination of the maximum punching shear resistance. The fact that the calculation of such an important value is still clearly empirical has met with criticism from many experts in recent years. Consequently, a new design model for the calculation of the maximum punching shear resistance, based on the critical shear crack theory was developed. The second generation of the Eurocode 2 (prEC2) introduces a more accurate and sophisticated design model for the determination of the upper limit of the punching shear capacity and considers several parameters. The main aim of this paper is to describe the new methodology of calculation of the maximum punching shear strength and the parameters that could influence it. The paper deals also with an assessment of the suitability of new model by comparing it with experimental results, that have been selected from a database of specimens that failed by punching at the level of VR,max.

A Fractal-Based Quantitative Method for the Study of Fracture Evolution of Coal under Different Confining Pressures

To study the dynamic crack evolution process of loaded coal from the perspective of fractals, we carried out in situ industrial CT scanning tests of loaded coal under different confining pressures, visualizing loaded coal fracturing. Combined with fractal theory, the temporal and spatial evolution law of coal cracks is described quantitatively. The results provide two findings: (1) from the perspective of two-dimensional images and three-dimensional space, the evolution characteristics of cracks in coal under different confining pressures were basically the same in each loading stage. During the loading stages, the cracks exhibited a change rule of a slow reduction, initiation/development, rapid increase, expansion, and penetration. (2) The fractal dimension of coal was calculated by introducing fractal theory, and its change law was in good agreement with the dynamic changes of the cracks, which can explain the influence of the confining pressure on the loaded coal. The fractal dimension showed three stages: a slight decrease, a stable increase, and then a significant increase. The larger the confining pressure, the more obvious the limiting effect. Thus, our approach provides a more accurate method for evaluating the spatial and temporal evolution of cracks in loaded coal. This study can be used to predict the instability failure of loaded coal samples.

Experimental investigation of punching shear behavior of flat slabs supported by rectangular columns and loaded with various load patterns

AbstractThe paper presents the results of an original experimental program that was focused on punching shear behavior of flat slabs supported by rectangular columns with a column rectangularity index cmax/cmin = 1.0, 4.33, and 6.33 and slabs supported by elongated columns that were loaded by four different load patterns. Seven isolated flat slab specimens with a thickness of 200 mm were tested until their failure. An effect of the column geometry and the way of the flat slab loading on punching shear capacity of slab‐column connections were investigated. The obtained experimental results were confronted with predictions carried out with the design provisions from code of practice EC2 (2004), ACI 318‐19, and prEC2 (2021) and the original Critical Shear Crack Theory (CSCT) (2008) model developed by Muttoni. Experimental results confirmed an effect of column rectangularity on punching shear resistance when a value of shear strength ratio Vtest/Vmodel was below one in the specimens with cmax/cmin > 2. The highest punching resistance was achieved in slab specimen with loading pattern x/2y where x is an axis along the column dimension cmax. The lowest capacity was achieved with a loading pattern 9x/y where 90% of the load flew perpendicular to the axis “y” parallel with cmin. The most accurate and balanced predictions provided CSCT (2008) model.

Punching performance of flat slabs with openings accounting for the influence of moment transfer and shear reinforcement

The arrangement of openings adjacent or near to slab-column connections is very common practice in flat slab design due to a number of advantages for technical installations. Such location is however conflicting with the most critical region of the slab, where punching shear failures may develop and typically govern the design at ultimate limit state. This requires in many cases arranging shear reinforcement to enhance the performance of the connections both in terms of resistance and deformation capacity. Such shear reinforcement is in addition particularly useful when unbalanced moments are transferred from the slab to the columns, which is a phenomenon typically detrimental for the punching shear resistance of inner connections. Despite the practical relevance of this case, there is currently no experimental evidence on the response of shear-reinforced slab-column connections with adjacent openings and moment transfer. Design is thus performed on the basis of simplified rules, modifying the resistance of connections without openings. In the present study, a comprehensive test programme addressed at this issue is presented in an effort to improve the current state-of-knowledge. Five slabs representing several practical cases and potential arrangements of shear reinforcement were tested. The experimental results are investigated in detail and compared to codes of practice, highlighting a number of deficiencies of current simplified rules. The phenomena is finally investigated on the basis of the mechanical model of the Critical Shear Crack Theory, showing a general frame for modelling and design of such detail.

Confiabilidade das prescrições normativas para dimensionamento à punção

Abstract This paper presents a reliability analysis of the punching shear of flat slabs without shear reinforcement. The evaluation is performed for the codes ACI 318, Eurocode 2, Model Code 2010, and ABNT NBR 6118:2014. Six models were used for predicting the punching strength, the design models, the Critical Shear Crack Theory (CSCT), and a Nonlinear Finite Element Analysis (NLFEA) model. Reliability analysis was performed to evaluate the safety level of code provisions. Design code provisions were evaluated in terms of sufficient reliability criteria based on target reliability β=3.8. This target reliability was based in the Model Code 2010 criteria. This criterion represents an acceptable value level of safety in design of structures. The results showed that the reliability indexes β presented satisfactory for all slabs designed by the Model Code 2010. However, this paper also shows some of the tested slabs presented reliability index below 3.0, being the ACI 318 the code with the lowest reliability index.

Effect of notch and stress ratio on Very High Cycle Fatigue characteristics of the carburized 17CrNi high-strength steel and life prediction

In order to investigate the notch effect on the structural characteristics of the carburized 17CrNi high-strength steel in the very high cycle fatigue (VHCF) loading, the axial tests with the stress ratio (R) of ‒1 were performed and the S-N characteristics were studied. The microscopic observation revealed that surface induced failure was the only failure mode. Further, the effect of the notch was investigated: Based on the small crack theory, the calculation of the fatigue notch factor (Kf) was performed and has shown that Kf is slightly less than the theoretical stress concentration factor (Kt). Then, Kf was used to study both the notch effect and stress ratio effect on fatigue life. Finally, the life prediction model associated with R and Kf was established and the calculation results are valid according to the good agreement with the experimental data.

Numerical Study of the Plastic Zone at the Crack Front in Cylindrical Aluminum Specimens Subjected to Tensile Loads.

Cylindrical specimens are of great interest in analyzing mechanical elements' behavior and investigating phenomena with biaxial loads. It is necessary to identify the behavior of the crack front along the thickness to interpret these results, which are usually based on the hypothesis of a straight crack and the observation of the outer face of the crack front. Based on the work carried out on compact tension type specimens, this work proposes adapting this methodology to cylindrical specimens, adapting the previous finite element models. Cylindrical specimens provide an asymmetric behavior influenced by the radius, where the CT (compact tensile) specimen can be considered the extreme infinite radius case. Combinations of the load level and radius values help us simulate the crack's behavior under intermediate hypotheses between a plane crack theory and a three-dimensional one. The plastic strain around the crack front will be analyzed as a function of the thickness and the load level applied. The results allow us to validate the numerical methodology and establish the differentiated behaviors of the plastic zones close to the outer and inner radii.

Numerical and analytical investigations on punching shear performance of UHTCC-enhanced RC slab-column joints

The excellent tensile strain-hardening behavior of ultra-high toughness cementitious composite (UHTCC) makes it applicable for enhancing the punching shear performance of reinforced concrete (RC) slab-column joints. However, construction of an entire slab-column structure employing UHTCC would inevitably lead to uneconomical designs. To balance the economic benefits with the punching performance, utilizing UHTCC in the core region of a slab-column joint is a promising approach. In this study, the impact of UHTCC application range (UAR) on the punching shear performance of UHTCC-enhanced RC slab-column joints (USCJs) was investigated, and an approach for determining the optimal UAR was also presented. Two USCJ specimens with different UAR were tested, and experimental results were compared with the counterpart numerical results to validate the finite element (FE) models. Twenty FE USCJ models with different UAR were established. Then the impact of UAR on development of critical cracks, ultimate resistance, and ductile behavior was examined. Analytical approaches based on the critical shear crack theory as well as on the combination of critical shear crack theory and yield line theory were adopted to predict the ultimate and flexural resistances, respectively. The failure mode was determined by comparing these two resistances and considering the ductile coefficient, based on which the effect of UAR on the failure mode was determined. The results show that the location of critical shear cracks and the appearance of flexural cracks vary with UAR. By increasing UAR, the ultimate resistance increases, but the ductile coefficient first increases and then slightly decreases. Provided that the UAR is increased to some extent, the growth rate of the ultimate resistance evidently slows down and the ductile coefficient peaks, indicating the optimal UAR considering both the economic efficiency and the punching performance. The presented approach shows promise for determining the optimal UAR in practical engineering designs.

Sudden column removal in tall buildings with flat slabs supported on core and perimeter columns

This paper focuses on robustness considerations of tall buildings with reinforced concrete flat slabs supported by a central core and one row of perimeter columns. This layout is commonly used in office and residential buildings to reduce storey height and maximise natural daylighting. The core and lateral bracing of tall buildings is generally less sensitive to local failure than the secondary load transfer system provided by the floors and perimeter columns, considering the high vulnerability of perimeter columns to accidental actions and punching of the slab around the supports. This paper analyses sudden corner and edge column removal situations in slab-core-perimeter column systems using dimensions and loading representative of current tall building design and construction, looking at potential punching at the connections and flexural failure in the slab. The dynamic punching model previously developed by the authors, was validated in this work for further cases of punching around edge columns and slabs with low amount of flexural reinforcement. The dynamic punching model is based on the Critical Shear Crack Theory for quasi-static punching and the Ductility-Centred Robustness Assessment method. A simplified level of approximation is proposed for a preliminary dynamic punching check during the conceptual design stage to optimise the position columns and level of flexural and punching reinforcement needed. The approaches proposed are consistent with Model Code 2010 and can be used to arrest the horizontal propagation of failure in the slab. The analyses of the case studies in this work showed that removal of an edge column adjacent to a corner column can be critical and alternative robustness design considerations are needed in this case.

A shear model for FRP reinforced concrete elements based on refined Critical Shear Crack Theory parameters

A shear model for FRP reinforced concrete elements based on refined Critical Shear Crack Theory parameters

A Study on the Distribution of Shear Forces Between Resisting Mechanisms in an RC Element Without Stirrups

This paper explores how the shear force distributes itself among the three main shear resistance mechanisms: shear resistance of the uncracked compressed chord, aggregate interlock, and dowel effect. Today’s dominating shear models, the critical crack theory (Muttoni et al. [1]) and the compression field theory (Collins et al. [2]) maintain that the main shear-resisting mechanism is aggregate interlock, while more recent studies (Marí et al. [3]), maintain that the main resistance mechanism is the shear resistance on the uncracked compression chord.
 In this paper FEM modelling is used to study a test carried out at the Universidad Politécnica de Madrid (UPM) to try to assign the shear force to the different shear mechanisms for different loading steps and elucidate what finally causes the failure of the structure. The results show that as load is increased the relative part of the shear force taken by the uncracked compressed chord increases until finally shear failure is reached when the principal tensile stress in the area located close to the load but towards the support reaches the tensile resistance of concrete, generating a crack that precipitates the failure of the beam.