Backbone Curves Research Articles

An effective multi-time series model of RC column backbone curve identification

Accurate identification of the backbone curves of reinforced concrete (RC) columns is key to engineering design and strengthening renovation. In view of the problems of high cost, long time, low accuracy, large dispersion of calculation results and discontinuous stiffness changes of the existing backbone curve identification methods, such as experimental method, finite element simulation method and semi-theoretical and semi-empirical method, it is proposed to transform the backbone curve identification problem into a multi-time series prediction problem. By introducing the attention mechanism and combining it with the bidirectional long short-term memory (BiLSTM), the backbone curve identification model (BC-ABiLSTM) is established considering the relationship between the front and back points of the backbone curves. Compared with the models for backbone curves with BiLSTM (BC-BiLSTM), long short-term memory (BC-LSTM), multilayer perceptron (BC-MLP), and the existing identification methods, the performance of the BC-ABiLSTM model is better, and the mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and R2 of the BC-ABiLSTM model on the testing set are 12.492 kN, 10.595 %, 20.838 kN and 0.9924, respectively, which provides a new method for accurate, efficient and cost-effective prediction of RC column backbone curve points under various cyclic loading levels.

A new simple masing-type soil nonlinear model considering modified damping and its application on KiK-net site response

In this paper, a series of simple Masing rules is first proposed for best fitting the shear modulus reduction and the damping ratio curves of soil based on the extended Masing rules and hysteretic damping formulation. A new masing-type nonlinear model is established and implemented in ABAQUS software based on the Matasovic back-bone curve and the new proposed Masing rules. To validate the practical applicability of the new model, the 1-Directional 3-Component nonlinear site response analysis for station KSRH10 (in Hamanaka, Hokkaido, Japan) is conducted. The numerically predicted results of the proposed nonlinear model are in excellent agreement with the recordings. The surface peak ground acceleration obtained by ABAQUS agrees well with the recording, which has a little difference of about 8.3% on average. The comparison between the proposed nonlinear model and the DEEPSOIL model indicate that the results of the former match better with recording to some extent, in term of acceleration time histories, spectral acceleration (SA) curves, and peak ground acceleration (PGA). The mean square error of acceleration time histories and SA curves obtained by the proposed model is smaller than the model in DEEPSOIL. The agreement with recording is improved by 10.8% compared with the DEEPSOIL model.

Experimental investigation of transition composite connections in historic style buildings

Historic timber buildings possess immense historical, artistic, and scientific value, but a few of them have survived after thousands of years of natural disasters and wars. Historic style buildings with modern construction material, imitating historic timber buildings forms, have emerged to inherit and promote traditional culture. To investigate the seismic performance of transition columns commonly used in historic style buildings, two full-scaled composite column transition (CCT) connections between steel reinforced concrete (SRC) square column and reinforced concrete (RC) circular column were designed and tested under invariable axial load and cyclic lateral load. Both failure patterns and force mechanism were studied based on the test process of the CCT connections. Then, the influence of axial compressive ratio on the mechanical behaviour of the CCT connections was assessed by looking at the hysteretic curves, backbone curves, characteristic loads, ductility, energy dissipation capacity and strength degradation. The results demonstrated that the failure patterns of the CCT connections were typical flexural failure, with the failure zone occurring at the upper column-root. The CCT connections exhibited excellent capacities of deformation and energy dissipation. As axial compression ratio increases, the failure of the CCT connection becomes more severe, leading to enhanced energy dissipation capacity. However, the strength and ductility of the CCT connection decrease. Based on the experimental results, an equation for calculating the lateral stiffness of CCT connections between SRC square column and RC circular column in historic style buildings was proposed, and verified to be accurate. The findings can provide necessary basis for the rational design and widespread application of historic style buildings.

Multi-gait snake robot for inspecting inner wall of a pipeline

In the field of pipeline inner wall inspection, the snake robot demonstrates significant advantages over other inspection methods. While a simple traveling wave or meandering motion will suffice for inspecting the inner wall of small-diameter pipes, comprehensively and meticulously inspecting the inner wall of large-diameter pipes requires the snake robot to adopt a helical gait that closely adheres to the inner wall. Our review of existing literature indicates that most research and development on the helical gait of snake robots has focused on the outer surface of cylinders, with very few studies dedicated to developing a helical gait specifically for the inspection of the inner wall of pipes. Therefore, in this study, we propose a helical gait that is suitable for the inner wall of pipes and meets the requirements of gas pipeline engineering. The helical gait is designed using the backbone curve method. First, we create a mathematical model for a circular helix curve with constant curvature and torsion, ensuring it is applicable to a snake robot prototype in a laboratory environment. Subsequently, we calculate the joint angles required for two conical spiral curves with variable curvature and torsion, establish a new model, and define the physical significance of the specific parameters. To ensure the feasibility of the proposed gait, we conduct experiments involving meandering and traveling wave motions to verify the communication and control between the host computer and the snake robot. Building upon this foundation, we further validate the mathematical model of the complex helical motion gait through simulation experiments. Our findings provide a theoretical basis for realizing helical movement with a real snake robot.

Large deformation analysis of spudcan settlement during operation

Jack-up rigs have been utilized to support booster stations in wind farms or to provide accommodation in oil and gas developments. In these scenarios, the dissipation of excess pore pressures and subsequent spudcan settlement during operation phase are of concern. However, predicting the spudcan settlement in naturally structured soil remains challenging. A large deformation finite element method, within the framework of effective stress analysis, has been developed to investigate the penetration and subsequent settlement of the spudcan footing. The inherent structure of cohesive soil and its degradation caused by spudcan penetration are described using the Structured Cam-Clay model. The large deformation approach is validated by comparisons with existing centrifuge tests. Parametric studies are then conducted with various operational loads and installation depths of spudcans. A backbone curve is provided, to estimate the history of spudcan settlement in kaolin with inherent structure. The distribution of excess pore pressures around the spudcan under different operation period is explored as well. A normalised dissipation curve at the largest cross-section of the spudcan during the operation phase is presented.

Experimental and analytical investigations on backbone curve models for RC shear keys under sequential seismic-tsunamic impacts

Reinforced concrete (RC) sacrificial shear keys play a crucial role in enhancing the structure resilience of coastal bridge against lateral impacts induced by seismic-tsunami scenarios. Existing researches have primarily focused on their performance under cyclic effects to simulate seismic impacts during earthquakes. However, their ability to withstand enduring forces under tsunami wave has been rarely studied yet. In this research, an experimental test was carried out to investigate the failure mechanism of RC shear keys under sequential cyclic-persistent effects, in which three typical failure modes of shear keys were considered. Various damage states were introduced to account for the possible damage levels after sustaining seismic impacts. The test results were analyzed by focusing on damage pattern, hysteretic behavior, peak capacity, and strain development, showing great distinctions with respect to different failure modes and corresponding damage stages. Furthermore, the analytical backbone curve models were developed based on the experimental test results. The presented models were validated using the typical strain-stress curve of reinforcement, and exhibited better applicability in characterizing the performance of shear keys under either cyclic or cyclic-persistent sequential effects, comparing to the other approaches that emphasizes on their seismic properties.

A Bayesian Multi-fidelity Neural Network to Predict Nonlinear Frequency Backbone Curves

Abstract The use of structural mechanics models during the design process often leads to the development of models of varying fidelity. Often low-fidelity models are efficient to simulate but lack accuracy, while the high-fidelity counterparts are accurate with less efficiency. This paper presents a multi-fidelity surrogate modeling approach that combines the accuracy of a high-fidelity finite element model with the efficiency of a low-fidelity model to train an even faster surrogate model that parameterizes the design space of interest. The objective of these models is to predict the nonlinear frequency backbone curves of the Tribomechadynamics Research Challenge benchmark structure which exhibits simultaneous nonlinearities from frictional contact and geometric nonlinearity. The surrogate model consists of an ensemble of neural networks that learn the mapping between low and high-fidelity data through nonlinear transformations. Bayesian neural networks are used to assess the surrogate model's uncertainty. Once trained, the multi-fidelity neural network is used to perform sensitivity analysis to assess the influence of the design parameters on the predicted backbone curves. Additionally, Bayesian calibration is performed to update the input parameter distributions to correlate the model parameters to the collection of experimentally measured backbone curves.

Experimental Study on Seismic Behavior of Newly Assembled Concrete Beam–Column Joints with L-Shaped Steel Bars

A novel concrete beam–column connection utilizing L-shaped steel bars is proposed to address the growing demand for prefabricated buildings and to ensure good seismic performance in such beam–column structures. After positioning two prefabricated beams with L-shaped tendons into the designated connection points at the top and bottom of the columns, concrete is poured into the post-cast section of the joint and the composite beam area, realizing a connection between the beams and columns. Quasi-static tests were performed on four combined backbone curves and one cast-in-place joint to investigate their failure modes and stress mechanisms. Through low-cycle repeated loading tests, it is found that measures such as increasing the area of the post-cast concrete in the joint area, the length of the L-shape, and the concrete strength in the composite beam area can effectively improve the bonding ability between the post-cast area of the joint specimens and the precast members, to improve the ductility performance, energy dissipation capacity, and bearing capacity of the joint specimens. The initial stiffness of the joint can be effectively improved by presetting the steel pipe in the column. Concurrently, the finite element method (FEM) was employed for parameter analysis. By integrating the test and FEM results, an equation for calculating the shear capacity of the connection was derived. The findings demonstrate that the hysteresis curve of the newly assembled joints is full, and its overall performance index is roughly the same as that of the cast-in-place joints. Additionally, enhancing the post-casting area of concrete, the length of the L-shaped bars, the concrete strength in the composite beam region, the axial compression ratio, or the steel tube dimensions can effectively improve the overall performance. The derived equation for the shear-bearing capacity of the connection satisfies design and application requirements.

Nonlinear characteristics identification of an impact oscillator with a one-sided elastic constraint

Impacting systems are widely used in many engineering applications, such as self-propelled robots, energy harvesting and percussive drilling, which exhibit rich and complex nonlinear phenomena. Among these applications, predicting nonlinearities and estimating system parameters are of great interest of nonlinear dynamics research community. Backbone curve is an analytical tool that captures the frequency–amplitude dependence of nonlinear systems. In this paper, we estimate the impacting stiffness of a single-degree-of-freedom non-smooth dynamical system qualitatively by using the backbone curve. It was found that an increase of the impacting stiffness may lead to lowering the backbone curve. An adaptive differential evolution algorithm with the Metropolis criterion is proposed to identify the parameters of the impacting system quantitatively using experimental data, which are consistent with our theoretical predictions. Finally, the identified parameters are verified, and the limitations of the backbone curve are drawn. The nonlinear characteristics identification method studied in this paper can be extended to other vibro-impact systems and is potentially applicable to structural health monitoring and robotic sensing.

Backbone curves of subgrade silty filler under intermittent train-induced loading

The loading intermittence duo to the time interval between adjacent passing trains is conducive to improving the dynamic stability of railway subgrade, but this intermittence effect is always ignored in existing experimental studies on the dynamic characteristics of subgrade fillers in which a continuous cyclic loading method was adopted to simulate the long-term train-induced loading on subgrade. This paper aims to study the backbone curves of subgrade silty filler under intermittent train-induced loading, considering the time interval between adjacent passing trains. By conducting a series of intermittent cyclic triaxial tests on silty filler, the backbone curves of each loading stage were constructed, and the effects of loading intermittence on the backbone curves were elaborated. The experiment results indicate that the loading intermittence enhances the resistance of subgrade silty filler to the dynamic loading and is conducive to the upward deviation of the backbone curves. The loading intermittence could effectively increase the ultimate value of dynamic stress amplitude that the silty filler could bear under cyclic loading, but has little effect on the maximum/initial resilient modulus. The backbone curves increase approximately linear under the states of plastic shakedown and plastic creep, but show significant nonlinearity after including the incremental collapse samples. Hyperbolic models for backbone curves such as H-D model and its improvement model could be adopted to characterize the backbone curves of silty filler under intermittent loading, and the normalization of H-D model was also discussed to integrate the influencing factors (i.e., moisture content and confining pressure) of the backbone curves.

Attention-Based Generative Adversarial Network Model for RC Column Backbone Curve Identification

Attention-Based Generative Adversarial Network Model for RC Column Backbone Curve Identification

A Unified Motion Modeling Approach for Snake Robot's Gaits Generated With Backbone Curve Method

A Unified Motion Modeling Approach for Snake Robot's Gaits Generated With Backbone Curve Method

Prediction on the seismic performance limits of reinforced concrete columns based on machine learning method

The drift ratio or lateral deformation is typically applied as the indicator in order to evaluate the earthquake-induced damage, one of the most important issues is to determine the seismic performance level limits. Therefore, this study presents to predict the seismic performance level limits of RC columns by using the machine learning method. Firstly, a test database of the backbone curves of RC columns was established after collecting 754 specimens under axial and lateral loads. Then the seismic performance level limits of all the collected columns were taken out as the input values of machine learning. The correlations among the geometric, mechanical parameters and the performance limits of RC columns were analyzed based on Pearson correlation analysis and mutual information method. Afterward, regression models of seven machine learning methods were established to predict the performance level limits of RC columns, while the hyperparameters of the machine learning models were optimized by the grid search and cross-validation methods. The generalization ability of the prediction models was verified and evaluated by using mean square error, mean absolute error, maximum error and R square, meanwhile, the accuracy of the applied methods was also analyzed. The seismic performance level limits of RC columns determined by the machine learning method can comprehensively consider the influence of geometric and mechanical parameters of RC columns. Combined with the earthquake-induced deformation of RC columns, the seismic damage of RC columns can be evaluated reasonably, which is of great significance for evaluating the seismic damage of building structures. The discussion on the prediction accuracy among different machine learning algorithms is also beneficial for the deformation prediction of other RC components.

Experimental Study of the Dynamic Characteristics of PVA-Amended Expansive Soils

Expansive soils are distributed across a wide area in China, and land transport and surface construction will inevitably involve these soils. To mitigate the deficiencies of single-method expansive soil modification, it is highly important to adopt the use of polyvinyl alcohol (PVA) to improve expansive soils and enhance the strength and toughness of modified soils. In addition, solidification technology can be utilized for the resource utilization of expansive soils. In this study, triaxial testing is employed to evaluate the mechanical properties of solidified soil. When the confining pressure is the same and with increasing PVA content, soil particles and PVA combine to form a cemented substance, which fills the internal pores of the soil samples, enhances the cohesion between soil particles, and improves the bearing capacity of the soil. The stress–strain curve for the modified soil first increases and then decreases. The shear strength peaks at a PVA content of 3%. Based on the improved soil with a 3% PVA content, GDS dynamic triaxial tests were carried out to investigate the effects of different confining pressures and frequencies on the dynamic stress–strain curves, dynamic modulus of elasticity, and variation rule for the damping ratio of the improved soil. The results show that the dynamic stress–strain curve for the improved soil increases with increasing confining pressure and frequency and that the dynamic stress–strain backbone curves exhibit significant nonlinearities at different frequencies and circumferential pressures. The dynamic elastic modulus increases with increasing confining pressure and frequency and decreases gradually with increasing dynamic strain. The initial dynamic modulus of elasticity increases with increasing envelope pressure and frequency but is less affected by frequency, and the damping ratio decreases with increasing confining pressure and frequency. Soil treatment can improve the pore distribution, inhibit the extension of soil cracks, and enhance soil compactness.

Lateral performance of cold-formed steel framed shear walls using slitted sheathing with stiffeners

Cold-formed steel (CFS) framed shear walls with steel sheathing are promising lateral-force-resisting members of mid-rise buildings in seismic regions. Previous studies have demonstrated that steel sheathed CFS framed shear walls have high shear capacity but some shortcomings, such as the low ductility caused by the premature damage of the frame and the shear buckling of the sheathing. This paper presents an experimental study on a novel type of CFS framed shear wall with slitted steel sheathing (CFS-SSWs), which uses longitudinal slits to change the failure mode of the sheathing so that the ductility of the wall can be improved; Meanwhile, stiffeners are utilized to enhance the out-of-plane stability of the slitted sheathing and the integrity of the wall. Six full-scale CFS-SSW specimens were tested under monotonic and cyclic lateral loading. Three types of stiffening approaches (Type I, Type II and Type III) were adopted for the walls. Test results were analysed to investigate lateral performances of walls under different stiffener arrangements, including failure modes, load-displacement hysteresis curves, backbone curves, stiffness and strength degradation, and energy dissipation capacity. The measured strengths of the walls in the tests were assessed using theoretical indexes. It is found that peak loads and energy dissipation capacity of stiffened walls are noticeably higher than those of the unstiffened wall. Type II and Type III are effective stiffening approaches that could mitigate the buckling of the slitted sheathing and enable the links between the slits to reach the full plastic strength. By connecting the stiffeners and studs through stiffener connectors, Type III has the most significant enhancement on the stiffness, strength and ductility of the wall.

Investigation of Small Strain Dynamics in Modified Aeolian Sand under Vibration Triaxial Conditions

By utilizing vibration triaxial tests, this study analyzed the effects of various factors, such as confining pressure, consolidation ratio, and silt content on the elastic modulus and damping ratio of silt-modified aeolian sand under conditions of minor deformation. The results indicate that with increasing confining pressure and consolidation ratio, the dynamic elastic modulus of improved aeolian sand gradually increases, while the damping ratio decreases progressively. The dynamic elastic modulus growth rate of untreated aeolian sand demonstrates a positive correlation with confining pressure, while the corresponding rate for the modified aeolian sand by adding cement and silt exhibits an inverse correlation with confining pressure. As dynamic strain increases, the dynamic elastic modulus decreases and approaches a stable value. The damping ratio rises at a diminishing rate and eventually stabilizes as dynamic strain continues to increase. The dynamic stress-strain backbone curve of the modified aeolian sand follows a theoretical hyperbolic model, while the small strain dynamic behavior is consistent with the Hardin-Drnevich model.

City-scale buildings damage estimation based on broadband physics-based ground motion simulation of 2021 Ms 6.4 Yangbi, China, earthquake

This article proposed a computational workflow for city-scale building damage estimation based on broadband physics-based ground motion simulation. The dynamic stiffness matrix method in frequency-wavenumber domain is employed for broadband physics-based ground motion simulation of finite fault along with site response correction using equivalent-linear site response analysis approach. With simulated ground motion, seismic response of buildings, using multi-degree of freedom model, is simulated using nonlinear time history analysis, and building damage is evaluated based on a trilinear backbone curve of story’s nonlinear force-drift model. Main advantage of the framework lies in the employed dynamic stiffness matrix method for ground motion simulation, which can efficiently generate broadband ground motions in perfect parallel and naturally capture the physics of finite fault source, propagation path, and spatial variability characteristics of ground motion. To demonstrate the salient features of proposed workflow, the 2021 Ms 6.4 Yangbi earthquake is simulated with frequency resolution up to 20 Hz, and seismic damage of buildings in Yangbi county are estimated. Results show that most traditional wood-adobe structures suffer moderate to severe damage, and engineered seismic buildings (mostly RC frame) in Yangbi county suffer minor damage, which agrees with field investigation results.

An efficient framework for structural seismic collapse capacity assessment based on an equivalent SDOF system

Assessing the structural collapse capacity efficiently and accurately is a key issue in earthquake engineering. Here, an efficient framework for structural seismic collapse capacity assessment based on an accurate equivalent single-degree-of-freedom (ESDOF) system is proposed. The corresponding ESDOF system is calibrated by matching the cyclic static pushover (SPO) curves of a more complex multi-degree-of-freedom (MDOF) system (e.g., high-fidelity finite element models) through a meta-heuristic optimization method. In this way, both the backbone curve and hysteretic characteristics (the stiffness and strength deterioration, and pinching behavior) of the complex MDOF system are considered in the corresponding ESDOF system. Then, incremental dynamic analysis (IDA) is carried out to assess the structural seismic collapse capacity using the ESDOF system instead of the corresponding MDOF system to improve the computational efficiency. The efficiency and accuracy of the proposed framework have been validated through three case studies, including a bare reinforced concrete (RC) frame, a steel frame, and an infilled wall RC frame. These results affirm that the proposed framework can accurately and efficiently assess the collapse capacity of low-rise bare and infilled RC frame structures, as well as steel frame structures.

Seismic performance of cold-formed thin-walled C-shaped steel composite wall with fireproof straw boards cladding

ABSTRACT In order to study the seismic performance of cold-formed, thin-walled C-shaped steel composite wall, a set of cold-formed thin-walled C-shaped steel skeleton structure and a set of composite wall covered with fireproof straw boards on both sides were tested with a low cyclic alternative load. The seismic performance indexes, such as bearing capacity characteristic value, lateral stiffness, ductility coefficient, energy dissipation coefficient and stiffness degradation, were analysed by obtaining the backbone curves of each group of specimens. The effects of fireproof straw boards on the seismic performance of the composite wall were compared, and a mechanical analysis model of the cold-formed thin-walled C-shaped steel composite wall was established by using ANSYS/structural finite element software. The results show that the damage patterns, backbone curves and capacity characteristic values of the finite element model are in general agreement with the tests. The bearing capacity and lateral stiffness of the light steel skeleton structure without boards is very low, while the bearing capacity of the composite wall with straw boards on both sides is significantly increased. The lateral stiffness increased by 10.76%, the ductility coefficient increased by 27.34% and the energy dissipation coefficient decreased by 45.8%.

Modelling of bidirectional functionally graded plates with geometric nonlinearity: A comparative dynamic study using whole domain and finite element method

Present work attempts to study the nonlinear dynamic behaviour of bidirectional functionally graded plates (BFG) along with unidirectional functionally graded plates (UFG). For BFG plates the material is graded along the thickness and length simultaneously and two types of UFG plates are considered namely thickness-wise (TFG) and length-wise (AFG) plates. The dynamic problem is formulated using two different methods namely, whole domain method and finite element method. The constitutive relation for the former is generated using classical plate theory whereas Mindlin plate theory is used in the later. Geometric nonlinearity is addressed here by using Von Karman type strain-displacement relation. Both clamped and simply supported boundary conditions are considered and the plate is assumed to be under action of uniformly distributed external load. The results of free and forced vibration analyses are presented as backbone curves and frequency response curves respectively. The results show that all three plates exhibit hardening type nonlinearity. It is also seen that the effect of material gradation parameters is more profound in simply supported plates compared to clamped plates. Specifically, these parameters do not seem to have much effect on BFG clamped plates in free vibration. The outcome of the analysis is compared with those in existing literature and fair agreement is observed between them.