Rigid Body Spring Model Research Articles

Prevention of concrete breakout failure of expansion anchor in tension by post-installed reinforcement: Discrete analysis and experiment

Concrete breakout failures with acutely damaged concrete are one of the main problems caused by expansion anchors under tensile loading. In this study, the prevention of concrete breakout is investigated by post-installed reinforcement (PRs). Experimental and numerical studies were conducted to look into the effect of the PRs on the expansion anchors subjected to tensile loads. The 3D Rigid Body Spring Model (RBSM), which is based on discrete analysis at the mesoscale, was used as supporting numerical research. On pullout capacity, displacement, failure mechanism, and concrete breakout geometry, both experimental and numerical analyses were undertaken. The numerical analysis also looked at internal stress, strain, and concrete cracking. In general, the anchors with the PRs had steady displacement (ductile) and less brittle failure compared to the anchors without the PRs. The significant finding was in the failure mode, where severe concrete damage and concrete breakout failures were prevented by the PRs. The internal tensile stress of concrete was concentrated around the wedges of the anchors (interlocked area). The contribution of the PRs was shown by high strain values at around their mid-length. Additionally, due to the PRs, concrete cracking was less, mostly generated in the region between an anchor and its PRs. The utilization of PRs could be a method to protect concrete from breakout failure.

Bond behavior simulation of deformed rebar in fiber-reinforced cementitious composites using three-dimensional meso-scale model

Fiber-reinforced cementitious composites (FRCC) can effectively develop the bond ductility of deformed rebar due to the high tensile resistance and strain capacity. This study presents a numerical method to evaluate the bond behavior of deformed rebar in FRCC based on 3D rigid body spring model (3D RBSM). Beam elements are used to model the rebar and the link elements are used to connect beam elements with RBSM elements as matrix. The same local bond-slip relationship for rebar is assigned at the link elements for both the simulation cases of plain mortar and FRCC. The model could properly simulate the single fiber to mechanical behavior of FRCC and the bond performance of rebar in FRCC. The results revealed that discrete fibers are the principal factors that preventing the splitting bond crack propagation and the stress propagation suggests the presence of high local bond stress around the rebar, improving bond ductility.

3D mesoscale simulation of the influence of corrosion on loss of tension stiffening in reinforced concrete

Corrosion-induced bond degradation leads to changes in deformation characteristics, cracking patterns, and loss in tension stiffening in structural members. Since the induced damage is dependent upon multiple inter-related parameters, prediction of post-corrosion deformation behavior requires sophisticated numerical simulations. This study integrates corrosion expansion and bond degradation models into a discrete analysis framework, 3D RBSM (Rigid Body Spring Model), to simulate post-corrosion loss of tension stiffening. Uniaxial tensile loading is applied to reinforced concrete models with different degrees of corrosion to obtain plots of load versus average strain and surface cracking patterns. Simulated surface cracking patterns due to corrosion and uniaxial loading in uncorroded and corroded models are similar to experimental results. As the degree of corrosion increases, the number of transverse cracks on the concrete surface decrease and the load at first cracking also decreases. Further, internal stress and bond stress investigation directly illustrate the decrease in stress transfer from reinforcing bar to concrete due to corrosion.

Mesoscopic simulation of crack propagation and bond behavior in ASR damaged concrete with internal/external restraint by 3D RBSM

One of the most serious serviceability concerns for reinforced concrete (RC) structures is expansion and cracking resulting from the alkali-silica reaction (ASR), which has a negative effect on material properties as well as the bond between reinforcement and surrounding concrete. In a typical RC member, ASR induced concrete expansion and cracking are restrained by internal reinforcement as well as the boundary conditions. The mechanism is complex and difficult to understand through experimental study, so predicting the residual capacity of a damaged RC structure is not easy. In this study, the authors use a 3D Rigid Body Spring Model (RBSM) comprising mortar, aggregate and steel elements and which is able to simulate ASR expansion in reinforced concrete. To study the complex interactions among multiple parameters and quantify the effect of ASR damage on structural behavior, previously reported experiments on ASR induced expansion under internal and external restraint are simulated, along with experiments on pullout behavior after ASR expansion. The effect of restraints on macroscopic ASR expansion is well modeled in each case, and how the development of internal stresses and concrete cracking influenced by the restraint can be explained from the simulations. The simulations enable discussion of the number of ASR-induced cracks and the internal stress condition in various cases. The peak bond strength of concrete with different ASR damage levels, as reported in pullout experiments, is predicted accurately and the load-displacement curves of ASR damaged concrete are discussed.

Investigating the effect of rebar corrosion order and arrangement on cracking behaviour of RC panels using 3D discrete analysis

In real structures, corrosion cracking patterns tend to be complex as a result of congested rebar arrangements and non-uniform corrosion distribution. It is challenging to understand the internal corrosion cracking behaviour based only on the limited amount of visible surface cracks. The present study attempts to use a meso-scale discrete element method, the three-dimensional rigid body spring model (3D-RBSM), to simulate factors that affect corrosion cracking. Factors considered in reinforced concrete panels with multiple corroded rebar includes, corroded rebar location, corrosion order among rebars and rebar arrangement. Three different cases are simulated and the results are compared with previously published experimental results. In one set of simulations, the non-uniform rebar corrosion profiles obtained in the experiments are utilized, with the results showing similar cracking patterns to the experimental ones. In a second set of simulations, uniform corrosion is assumed so as to conduct a parametric study of the same specimens for an accurate understanding of each influencing factor. It is observed that when all rebars corrode simultaneously, the initial cracks propagate along the outer rebars because this is where the confinement effect is minimum. Cracking along inner rebars is delayed due to strong compression zone resulting from mechanical interaction among corroded rebar stresses. However, this compression zone is reduced when the rebars corrode in two stages and cracking occurs at all the rebar locations. Cracks that initially form along the inner rebars can close up when corrosion of the outer rebars occurs later.

Explicit Dynamic Analysis by a Rigid Body-Spring Model of Impact Loads of Artillery on Middle Age Fortifications

The development of artillery in Europe at the end of the Middle Ages brought a necessary change in military architecture. This change was a radical rethinking of the entire geometry and architectural design of city walls which required an increase in thickness to resist repeated artillery strikes. The damage due to the impact loads on Middle Age fortification walls is analyzed herein with explicit dynamic analyses. This study was developed both with finite element models and an innovative rigid body-spring model with diagonal springs (RBSM), showing the different peculiarities of these two different approaches and how their results can be integrated. The numerical models clearly showed that the presence of an inner core of softer material tends to modify the impact effects by reducing the degree of damage at the expense of an extension of the damaged area.

Macroscale modelling of the orthotropic shear damage in the dynamics of masonry towers by RBSM

The peculiarity of a rigid body-spring model (RBSM) is exploited to predict and explain a specific damage pattern and failure that is often observed in ancient masonry towers subjected to seismic events. In fact, the full understanding of the frequent appearence of a vertical pattern of cracks along the height of these buildings, which could be viewed as a macroscopic mode II shear fracture, would require to overcome the macroscopic approach based on the standard Cauchy solid continuum. The research focuses on the orthotropic shear response of the masonry material, related to its bond/texture pattern, which is here accounted by a RBSM that allows to assign, heuristically, a different shear strength and internal friction, parallel and normal to the plane of the mortar bed joints. This specific feature, in the context of a set of full dynamical analyses, appears to be a key to predict the crack pattern and failure of an idealized masonry tower, in accordance with the surveys of real towers subjected to strong ground motions.

Estimating corrosion levels along confined steel bars in concrete using surface crack measurements and mesoscale simulations guided by model predictive control

In corroded reinforced concrete (RC) structures, there is a need to understand the degree of internal corrosion of the reinforcing bars in order to evaluate residual performance and ensure a rational maintenance regime. The authors have developed a computational approach for estimating the distribution of corrosion along the length of a reinforcing bar from the observed surface crack widths. The approach is based on mesoscale simulations of reinforced concrete, using rigid-body-spring models (RBSM), guided by Model Predictive Control (MPC). The current study extends that research to account for differing (smaller) crack openings, multiple instances of localized corrosion, and added confinement due to the presence of stirrups. Accuracy of the proposed approach is demonstrated through comparisons with laboratory tests of steel corrosion within concrete. The crack distribution observed on the concrete surface is automatically reproduced by optimized application of internal expansion within the mesoscale model, from which the corrosion distribution is estimated. The estimated corrosion distribution is accurate when compared to the measured corrosion of bars removed from the test specimens. In the case of specimens with stirrups, crack distributions and openings are accurately simulated by the MPC-RBSM system. Estimated corrosion levels are close to the measured values with some variations. The main reasons for these variations are the greater crack widths and higher corrosion levels in the stirrup-confined specimens. The simulated crack patterns are similar to those observed on the experimental specimens, indicating that specimen damage is simulated well. The internal stress and cracking distributions simulated by this method of meso-scale discrete analysis provides useful information for evaluating damage level that cannot be observed at the surface.

Interface Stress Element Method, Rigid Body Spring Model and Applied Element Method

Interface Stress Element Method(ISEM), Rigid Body Spring Model(RBSM) and Applied Element Method(AEM) are typical connected discrete element methods derived from the same origin. Although there are many differences in their model compositions, expression forms, development paths and application situations, the three methods are closely related. In this paper, the commonalities and differences among ISEM, RBSM and AEM were expounded from five aspects: model composition, stiffness matrix for interface, formula for inter-element stress, theoretical system and analysis procedure. They discretize the domain with rigid blocks, but connect them using interface layers, distributed spring pairs and multiple spring pairs respectively. For homogeneous isotropic materials, the stiffness matrixes for RBSM are equal to that for ISEM, and there are only four items different in the stiffness matrix for AEM. The formula for inter-element stress of RBSM and AEM can be expressed by that for ISEM. The relationships among ISEM, RBSM and AEM were further clarified. RBSM and AEM are both special cases of ISEM. They can be incorporated into the theoretical system of Interface Stress Element Method. The three constitute a unified method family.

Mechanism of drying-induced change in the physical properties of concrete: A mesoscale simulation study

Although many studies have found that drying alters the mechanical properties of concrete, the mechanism behind this change remains unclarified. The aim of this study is to elucidate the mechanism of change in properties of concrete after drying through the numerical calculation: a 3D mesoscale rigid-body-spring model (RBSM) with three phases, i.e. mortar, aggregate, and the interfacial transition zone while considering the properties changes of mortar due to drying. Based on the RBSM results, it is concluded that the change in compressive strength due to drying and heating is determined by a balance of the impact of drying-induced microcracking around coarse aggregates and the change in mechanical properties of the mortar due to drying. These mechanisms change the applied load required to reach the critical crack width and distribution, at which rim of the specimen begins to isolate from the core region and the load sustained by the rim decreases.

A proposal for an approach for meso scale modeling for concrete based on rigid body spring model

Existing meso-scale models of concrete need to refine the mesh grids of aggregate and cement mortar, which may greatly reduce the computational efficiency. To overcome this problem, a novel meso-scale modeling strategy, which is based on rigid body spring method and Voronoi diagram, is proposed in this study to establish the meso-scale model of concrete. Firstly, establish numerical aggregate models according to user-defined programs. Circle aggregates are adopted due to their high efficiency in generation and packing process, and the grading of aggregate are determined according to the distribution curve proposed by Full and Thompson; Secondly, extract the centroids of aggregates, and then develop the Voronoi diagram in which aggregate centroids are defined as initial scatters; Finally, establish the rigid body spring model for concrete based on the Voronoi diagram. Aggregates are represented by rigid blocks, and assumed to be unbreakable. Cement mortar is concentrated into the interface between adjacent blocks and represented by two uniform springs. The number of grids is consistent with that of aggregates in specimens, and no mesh-refinement of aggregates and cement mortar is required. The accuracy and efficiency of the proposed modeling strategy are firstly identified by comparing the numerical results with the experimental ones, and then the applicability of the proposed strategy with different volume percentage occupied by aggregates is investigated.

Plate-Springed Parallel Elastic Actuator for Efficient Snake Robot Movement

The design methodology of a plate-springed parallel elastic actuator (PSPEA) for the efficient movement of planar snake robots is presented. The stiffness, which refers to the relationship between the resilience moment and the joint angle, of the plate spring was first designed using a rigid body spring model. The modeled stiffness was then verified via a simple test rig. Combinations of spring stiffnesses that minimize the energy consumption of each joint at different velocities were obtained using dynamic simulation. Experiments using a planar six-link PSPEA-based snake robot were performed via sensors installed in the servomotors to measure torque and speed, and a motion-tracking system was utilized to measure the moving distance. True efficiency was evaluated using the cost of transport criterion, which was later compared with the dynamic simulation results. Despite its compact design, it was observed that the proposed PSPEA improved the energy efficiency of the snake robot by a maximum of approximately 50%.

Mesoscale simulation of pull-out performance for corroded reinforcement with stirrup confinement in concrete by 3D RBSM

The confining effect of concrete cover and stirrups reduces the rate of bond deterioration due to corrosion. However, the large dispersion in recorded experimental data makes it difficult to clearly separate the influence of cover depth and stirrup confinement on bond degradation. This study utilises the discrete 3D Rigid Body Spring Model (RBSM) to conduct a meso-scale investigation regarding the effect of cover thickness and stirrup confinement on internal crack evolution and pull-out behaviour in corroded reinforced concrete models. The simulation scheme is divided into two stages. In stage 1, different degrees of corrosion are introduced, producing cracking in the cover concrete; in stage 2, the corroded main reinforcement is pulled out from the damaged concrete. 3D RBSM is advantageous because the concrete is randomly meshed to reduce mesh bias on crack propagation and the actual geometry of the deformed bars is modelled. The simulation results clarify that the presence of thicker cover delays crack initiation but increases the rate of crack opening. Stirrups do not have any significant effect on crack initiation but effectively restrict crack growth. An investigation of the internal stress in the simulation models shows that tensile stresses generated in stirrups during corrosion are responsible for reactionary confining pressure that restricts crack propagation. Load-displacement curves show reductions in pull-out capacity, stiffness and ductility with increasing corrosion damage. The relative influence of crack opening and stirrup volume on the rate of bond degradation with respect to average surface crack width are discussed and compared with published experimental results and an empirical equation.

Seismic response of a masonry church in Central Italy: the role of interventions on the roof

The seismic response of a medieval church in Central Italy is analyzed considering the two roof configurations, i.e., reinforced concrete and timber roofs, that the church had in different periods of its existence. Structural interventions and changes are common in the churches of this territory, where frequent earthquakes put these buildings at risk. The church studied here, St. Salvatore in Acquapagana (Serravalle di Chienti, province of Macerata), was damaged by the 1997 Umbria-Marche and the 2016 Central Italy earthquakes. Between these two seismic events, the church was repaired, and the concrete roof was substituted with a lighter timber roof. To investigate the influence of this change on the seismic response, a study was performed at the building and façade macroelement scales using the finite element model and rigid body spring model, respectively. For each approach, the two roof configurations were considered, and two strong motion records, from September 26, 1997, and October 30, 2016, were applied. The results show that the concrete roof improves the box-like behavior, but it increases the vulnerability of the masonry structures, characterized by a limited tensile strength. Conversely, in the timber roof configuration, the most vulnerable areas of the structure are the intersections between structural elements.

Discrete mesoscale analysis of adhesive anchors under tensile load taking into account post-installed reinforcement

The utilization of post-installed anchors is growing fast to connect both structural and non-structural members. Adhesive anchors are one type of post-installed anchors which are formed as threaded bars. They can be post-placed into concrete with the help of epoxy adhesive. On the one hand, improvement of the performance of post-installed anchors, unlike cast-in-place anchors, has not drawn attention much. On the other hand, due to the complexity of their performance, a numerical study can be a supportive method for the experimental study. This paper addresses the effect of post-installed reinforcement (PR) on the adhesive anchors under tensile loading in both experimental and numerical studies. Reinforcing steel bars as post-installed reinforcement (fully embedded in concrete) were used to ameliorate the performance of the adhesive anchors under tensile force. Rigid Body Spring Model (RBSM) was developed as a simulation that is based on discrete analysis at mesoscale. Pull-out capacity, displacement, failure mode, and concrete cone geometry were measured by the experiments and the RBSM simulation. In addition, internal stress, strain, cracking patterns were investigated by the RBSM simulation. Moreover, some comparisons were conducted through the existing standard. In general, PR assist the anchors to have higher pull-out capacities, lower displacement as well as leading smaller size of concrete cone failure. Due to PR, the internal tensile stress of concrete changed to compressive stress resisting greater pull-out force. The higher strain is obtained at near the top of the anchors and at the mid-span of PR. Furthermore, cracking patterns in concrete were mostly within the area between the anchor and PR. Post-installed reinforcement can be considered as a method to improve the performance of adhesive anchors under tensile loading. This is validated by the RBSM simulation, which agrees with the experimental results.

Estimation of internal corrosion degree from observed surface cracking of concrete using mesoscale simulation with Model Predictive Control

AbstractCorrosion of the steel reinforcing bars in concrete structures is one of the major maintenance problems. Corrosion results in expansive pressure on the surrounding concrete, which causes internal damage that may become visible as surface cracking. Such damage may degrade structural safety and serviceability. Effective maintenance requires the evaluation of residual performance based on estimates of spatially nonuniform levels of corrosion, which are typically obtained through surface measurements only. In this study, the authors have developed a simulation system for estimating the levels of internal corrosion along the reinforcing bar length from surface crack information. This innovative system is produced by integrating the technique of Model Predictive Control (MPC) with Rigid‐Body‐Spring Models (RBSM) of corrosion‐induced cracking at the concrete mesoscale. In this study, MPC controls the simulated surface cracks such that they match the observed cracks by optimizing the internal expansions of springs representing the steel‐concrete interface within the RBSM. The applicability of the system is verified using both synthetic crack width data and crack data collected from in‐house laboratory testing. In the laboratory testing, corrosion levels were quantified by 3D scanning of the extracted reinforcing bars. The simulation results agree with the corrosion measurements, demonstrating the potential of the MPC‐RBSM system for predicting the corrosion distribution along reinforcing bars using surface crack data.

Numerical Evaluation of the Perfobond (PBL) Shear Connector Subjected to Lateral Pressure Using Coupled Rigid Body Spring Model (RBSM) and Nonlinear Solid Finite Element Method (FEM)

An analytical investigation focusing on the concrete damage progress of the PBL shear connector under the influence of various lateral pressures, employing a coupled RBSM and solid FEM model was carried out. The analytical model succeeded in simulating the test shear capacities and the failure modes adequately. The internal failure process was also clarified; the two horizontal cracks occurred near the top of the concrete dowels through the hole of the perforated steel plate, and afterward, the two vertical cracks also initiated and propagated along with the shear surface. In a low lateral pressure case, the shear strength was determined by the vertical cracks propagated along the shear surface. While as the amount of applied lateral pressure increased, the shear strength of the two vertical cracked surfaces was enhanced, and the shear strength of the PBL was characterized by the occurrence of the splitting cracks and caused the splitting failure into the side concrete blocks. Moreover, the combined effects of lateral pressure and hole diameters were also evaluated numerically, and it was found that the increase in shear strength was more in a large diameter case subjected to high lateral pressure because of the wide compressive regions generated around the concrete dowel.

Numerical simulation of failure process of high-strength concrete using the discrete-element model

A two-dimensional mesoscopic model is presented for simulation of the failure process of high-strength concrete (HSC) confined by fibre-reinforced polymer (FRP). The model is based on the discrete-element method and modified rigid-body spring model, which were developed for simulation of the behaviour of normal-strength concrete, and is extended here to model HSC. Due to the fact that the mortar matrix and the interfacial layer in HSC are generally stronger than the strength of the aggregate, springs are designed in such a way that the crack can penetrate into the aggregate. To develop the confined model, FRP elements are connected to the basic model as rectangular elements, the connections of which are modelled together based on Hooke's law in cylindrical coordinates. Interfacial springs between FRP and concrete elements are designed based on the bond–slip model and the behaviour of concrete core under confining action provided by the FRP jacket. The failure behaviour of three unconfined and two confined HSC specimens was simulated by the proposed model. Analytical results are presented as stress–strain curves and crack modes, which were found to be in good agreement with experimental data.

A mesoscale discrete model for mechanical performance of concrete damaged by coupled ASR and DEF

Real concrete structures can suffer simultaneously from the alkali-silica reaction (ASR) and delayed ettringite formation (DEF), resulting in expansion of the concrete and surface map cracking. This damage can lead to serious durability problems. The respective effects of ASR and DEF have been studied, but the cracking behavior of concrete when they act together remains unclear. In this study, a three-dimensional rigid body spring model (3D RBSM) is used to simulate the cracking and mechanical property degradation of concrete under coupled ASR and DEF. A parametric study is conducted to understand various combinations of ASR and DEF. In line with previous studies by the authors on independent ASR/DEF damage, expansions caused by ASR and DEF are, respectively, introduced as strains at the mortar-aggregate interface and in mortar elements. Due to a confinement effect, specimens subjected to coupled expansion may suffer less expansion or cracking than when only one of the degradations is acting. The model clearly visualizes the cracking process and stress development as the degree of coupled expansion increases. More importantly, based on the simulated results, the interactions of the two types of expansion are revealed by correlating the degradation in mechanical properties with internal cracking behavior. Further, the confinement effect arising on application of the second type of expansion is quantitatively examined. While there is no significant change in stiffness, compressive strength in some cases increases with expansion as larger cracks close up under the confinement effect. This kind of investigation of coupled effects is difficult to quantitatively analyze through experimentation, but this work demonstrates that it is possible using RBSM simulations.

Numerical evaluation of the Perfobond rib shear connector (PBL) subjected to various constraints using Rigid Body Spring Model (RBSM)

Numerical evaluation of the Perfobond rib shear connector (PBL) subjected to various constraints using Rigid Body Spring Model (RBSM)