Load-displacement Response Research Articles

Experimental and Numerical Study of Static Behavior of Precast Segmental Hollow Bridge Piers.

To investigate the static performance of precast segmental hollow piers, two precast segmental hollow pier specimens were designed for static loading tests on the top of piers. The finite element model of precast segmental hollow piers was established by the finite element software Abaqus and verified based on the test results. Based on the experimental and finite element models, three optimal design solutions were proposed, and the calculation results of each solution were analyzed. The results show that precast segmental hollow pier mechanical behavior is similar to that of cantilevered bending members. The specimens present brittle damage characteristics after the destruction of the structure at the bottom of the pier pressure edge as the axis of the rigid body rotation. Following the test loading process, the bonding between the segments is good, except for the pier bottom damage surface of the rest of the bonding surface, which has no relative displacement. The calculation results of the finite element model are in good agreement with the test results and can effectively predict the load–displacement response of precast piers. Three optimized design solutions are proposed. The finite element simulation proves all three optimized design solutions show better overall ductility than the original solution and can effectively improve the performance of segmental precast hollow piers.

Temperature effects on the low-velocity impact of FML panels: Experimental and numerical analyses

This study aims to evaluate the impact damage of FML panels under the effects of elevated temperatures. Low-velocity impact tests were conducted experimentally on FML panels at impact energy levels of 5, 8, 10, 12, 13.5 and 15 J at room temperature. Finite element models of the FML with quarter and half symmetry were then developed using explicit nonlinear code LS-DYNA and validated against experimental results. The quarter model was sufficiently validated as it simulates identical results compared with the half model. The quarter and half models produced maximum percentage differences of 11.92 and 15.25% respectively in terms of the total energy absorption, along with respective 5.68 and 5.57% for the peak load. Thereupon, combined analysis on the same impact energy levels and temperatures of 30, 50, 70, 90 and 110°C were performed by employing the FE quarter model. The results indicate that an increase in temperature significantly affects the low-velocity impact response and impact resistance of FML. Load-displacement and deflection responses show pronounced loss of stiffness, toughness and resilience with increasing temperature. From 30 to 110°C, the energy restitution coefficient (ERC) decreases by roughly 0.2 while the load-bearing capacity drops by 45 to 50%. The degradation of FML is progressive in that it is less significant at a lower temperature range of 30 to 70°C yet severe at a higher temperature range of 70 to 110°C. Evidently, the impact damage of FML panels may be more severe in critical applications involving ranges of high temperatures.

Shear behavior of RC pile cap beams strengthened using ultra-high performance concrete reinforced with steel mesh fabric

Although pile cap bases of structures are the most significant element in the construction and one of the most difficult parts in strengthening applications, previous studies on this element, particularly strengthening, are quite limited. The most extensively utilized, highly efficient, and simple to implement solution is ultra-high performance concrete (UHPC). In this study, six-half scaled pile cap beams were prepared and experimentally tested. Three of them were strengthened with UHPC (one in shear with connectors only, one in shear with connectors and steel mesh fabric (SMF), and one in shear and punching with connectors and SMF), while the other three were not strengthened to explore the influence of side bars. The bottom bars of the all six beams were identical, consisting of main longitudinal tensile and secondary lateral reinforcement. The load-displacement response, ultimate carrying load, failure mechanisms, energy dissipation capacity, and shear ductility of pile cap beams were all thoroughly investigated. The results revealed that using side bar reinforcement and UHPC with various techniques significantly enhanced the shear strength and ductility of pile cap beams. Except for the specimen including additional internal side bars, there were no appreciable differences in the peak load of un-strengthened reinforced concrete (RC) pile cap beams. The gain in peak load was 59% due to use of side bars. The RC pile cap beam strengthened in shear and punching with connectors and SMF exhibited the highest peak load and the highest energy dissipation capacity among all tested specimens.

Deformation Behavior of Grouted Sleeve Wall Connector Under Shear Load in Precast Process of Concrete Wall

This study investigated the behaviour of grouted sleeve connectors under shear loads. Tapered Head Sleeve (THS) connectors were fabricated from mild steel pipes. Five test specimens and a control specimen were produced. Each test specimen comprised two walls, which were connected by THS. An incremental shear load was applied at the joint until the specimen failed. The behaviour of the specimens was analyzed based on the load-displacement response. The feasibility of THS as a wall connection was determined based on ductility ratio, failure mode, performance ratio, and serviceability ratio. THS required an embedded length of 8 times the bar diameter to generate sufficient bond strength. The specimens experienced bar dowel action, which led to a significant horizontal displacement with a ductility ratio of 27.5 to 55.9. The test specimens offered shear capacities comparable to the control specimen, with performance ratios close to 1.0. The service load was only 1/3 of the ultimate capacity, and thus THS was ineffective in resisting shear load. Shear keys would be required to strengthen the joint of the specimen.

Modular multistable metamaterials with reprogrammable mechanical properties

Owing to extensive potential applications in various engineering areas, the multistable metamaterials with remarkable mechanical properties have gained increasing interest from both academia and industry recently. However, the functionality of existing multistable metamaterials is hard to adjust once fabricated. To overcome the limitation, in this paper, we propose an idea of modular multistable metamaterial (MMM) with reprogrammable mechanical properties, which is assembled by unit cells with tunable snap-through behaviours. The unit cell is made by a dismountable bar and a fixed frame containing two bistable curved beams. By inserting the bar with different length into the frame, we can change the shape of curved beams and therefore tune the snap-through behaviour of the unit cell, which lies the foundation of its tunable multistabilities. We evaluate these tunabilities of geometry and mechanical properties of single unit cell by employing theoretical analyses and validate them by numerical simulations. The obtained quantitative results provide us the design guide for assembling of the MMM. We fabricate a certain number of components by 3D printing and assemble them as a unidirectional MMM to examine its reprogrammable macroscopic mechanical behaviours. We firstly investigate the tunable load–displacement responses experimentally and numerically; and then explore the tunable bandgaps through numerical simulations. Finally, we demonstrate the broader possibilities of assembly to form bi- and tri-directional, as well as gradient MMMs. The results presented in this paper have great significance for the design of modular metamaterials and expanding their application prospects in engineering structures.

Numerical investigation of the effect of particle gradation on the lateral response of pile in coral sand

This paper addresses the effect of particle gradation on the lateral response of pile in coral sand foundation through numerical method. Firstly, the parameters of Hypoplastic (HP) constitutive model were calibrated by a series of laboratory tests and show obvious difference in value between fine and coarse coral sand. Subsequently, a 50 g centrifuge test and 1g model pile test were carried out to verify the numerical model and calibrated parameters. Afterward, numerical analyses were systematically conducted to investigate the influence of particle gradation, buried depth, and relative density on the lateral response of pile. The lateral load–displacement response, deflection and bending moment of pile, and soil resistance were analyzed and discussed in detail. Numerical results show that the bearing capacity of pile and soil resistance in coarse sand are greater than those in fine coral sand when the relative density is 25 % or 50 %. However, when the relative density is 75 %, the bearing capacity of pile and soil resistance in fine sand present significantly greater values than those in coarse sand under higher lateral displacement level. Moreover, the difference in lateral response of pile between coarse and fine coral sand is more significant in looser sand or shorter pile.

Three-dimensional failure envelope of concrete dam shear keys

Shear keys provide interlocking mechanisms along the vertical contraction joints of many concrete gravity dams. The shear key ultimate shear capacity is typically estimated as a function of the friction and cohesion that could be mobilised across a 2D shear plane located at the base of the key when subjected to a normal confinement pressure, P. A two-dimensional response of dam monoliths and shear keys shearing-off at their bases, is assumed. However, evidence of 3D interlocking behaviour between dam monoliths and the possibility of different key failure mechanisms involving interacting axial, P, shear, V, moment, M, and torsion, T, indicates that typical empirical formulations could significantly overestimate the actual shear key capacity under floods and seismic loadings. This paper presents an evaluation of the load–displacement response of shear keys subjected to multiaxial loading via nonlinear finite element analyses. A concrete “Continuous Surface Cap Model” (CSCM), available in the computer program LS-Dyna, is first shown to best capture the experimental shear keys' ultimate and residual shear capacity responses among five constitutive models. The effects of the tensile strength, fracture energy, confinement pressure, friction coefficient, initial opening, and dilation conditions on the load–displacement response of keys are investigated. Failure envelopes considering the key multiaxial shear capacity with confinement pressure, P, moment, M, and torsion, T, are developed. The ratios between moment and shear, M/V, and torsion and shear, T/V, control the failure mechanism. Increasing these ratios significantly reduce the ultimate shear capacity.

Tensile low-cycle fatigue performance and life prediction of high-strength bolts

Monotonic tensile tests and tensile low-cycle fatigue tests have been conducted to explore the low-cycle fatigue life of high-strength bolts, which is an important property to guarantee the connections do not occur low-cycle fatigue failure before their connected members under earthquakes. Large-deformation performance and failure modes of bolts were numerically simulated based on the damage constitutive relation which was investigated by the tensile tests of smooth and notched specimens. The results show that complete uniaxial constitutive relation of the bolt material, namely 20MnTiB steel, and the displacement from tensile load response of smooth specimens in the numerical simulation can be better described by the Swift flow stress model. The GTN damage model of the steel was calibrated by tensile tests and finite element models of notched specimens. With the decrease of the notch radius, the tensile capacity of the notched specimen increases while the ductility gets worse. The calibration parameters of GTN damage model can be applied to simulate the load-displacement response and fracture behavior of notched specimens accurately. In order to obtain a more targeted GTN model under different stress states, the quantitative relation between equivalent plastic strain during nucleation and stress triaxiality was proposed, which provided an important reference for establishing fatigue damage models of various bolted joints in the numerical simulation. Both the fatigue failure modes of the bolts under cyclic displacement with constant amplitude and the fatigue life based on the tensile capacity degradation were obtained from the fatigue tests. The fatigue brittle fracture and plastic elongation of the shank are the two fatigue failure modes of the bolt. Typical regional characteristics are presented in the bolt fatigue fracture, with beach-like fatigue bands in the expansion area. Under different failure modes, the capacity degradation can better determine the fatigue life of bolts. The methods for predicting fatigue life were proposed based on cyclic displacement amplitude, equivalent stress amplitude and local plastic strain. A good prediction result was proved by the phenomena that the predicted fatigue life based on the cyclic displacement amplitude and local plastic strain was basically within the scatter band of 1.5. Moreover, the fatigue design parameters of bolts given by the equivalent stress amplitude method provide a reference for establishing a unified fatigue design theory.

Influence of weave architecture on mechanical response of SiCf-SiCm tubular composites

Due to their high resistance to radiation damage and elevated temperature, silicon carbide fiber-reinforced, silicon carbide matrix composites (SiCf-SiCm) are identified as potential cladding structures for use in nuclear reactors. In this study, four composite architectures with varying ply numbers along the thickness direction and different biaxial or triaxial plain weave orientations at either 45° or 60°, were systematically evaluated under various stress states to assess the influence of weave architecture on mechanical performance. Experiments were conducted on SiCf-SiCm composite tubes under tensile hoop, axial compression, and rotating flexural loading to evaluate the mechanical response and investigate the failure modes using high-speed imaging and digital image correlation (DIC) techniques. It was found that for tensile hoop burst and flexural loading, the braiding angle had the most significant influence on the strength of the composite, whereas the effect of fiber angle was more limited for compression testing. Under axial compression a unique failure mode where a microcrack nucleates and grows only to a length equal to the thickness of a single yarn was identified. This crack growth behavior is reflected as periodic oscillations in the load-displacement response. For both axial and hoop loading, regardless of weave angle and number of plies, failure always initiated parallel to the tube axis in a single yarn and the cumulative interaction of these microcracks lead to either axial burst or fracture at an angle to the tube axis along a yarn. These results point to the importance of customizing the design of tube architecture for enhanced performance in specified nuclear applications.

Effect of spontaneous-combustion coal gangue aggregate on axial performance of square concrete-filled steel tube stub columns

This work experimentally studied the effect of spontaneous-combustion coal gangue aggregate (SCGA) on the mechanical performances of the square concrete-filled steel tube (CFST) stub columns subjected to axial loading. The influences of the substitution level of SCGA and the steel tube thickness on the failure mode, axial load–displacement response, ultimate load, elastic stiffness, and ductile performance were investigated. Trial results showed that the reduction in the ultimate compressive load of the CFST stub columns at an SCGA substitution level of 50% and 100% is within 5.96% and 12.10% respectively, compared to the CFST specimens made of natural aggregate (NA). Moreover, the elastic stiffness of the columns made of SCGA declined by 4.58%–16.67% and 22.44%–24.20% and their ductility coefficient by 1.10%–14.76% and 8.04%–18.27% at an SCGA substitution level of 50% and 100% respectively. To extend the parametric range of the experiment, the finite element models were analyzed in detail for estimating the influences of the SCGA substitution level, the concrete strength, the yielding strength of the steel tube, and the diameter of the stub columns utilizing Abaqus software. The results demonstrated that influences of SCGA incorporation on ultimate compressive load of CFSTs with square section could be presented via concrete strength and confinement coefficient. The design equations described in standard GB50936 were comparable to predict the ultimate load of the square CFST stub columns according to the finite element modeling data and verified by experimental results, and could be used for the routine design of CFSTs with SCGA.

Towards understanding deformation and fracture in cementitious lattice materials: Insights from multiscale experiments and simulations

Tailoring lattice structures is a commonly used method to develop lattice materials with desired mechanical properties. However, for cementitious lattice materials, besides the macroscopic lattice structure, the multi-phase microstructure of cement paste may have substantial impact on the mechanical responses. Therefore, this work proposes a multi-scale numerical modelling method to simulate the deformation and fracture behavior of cementitious lattice materials, such that the influence of cement paste microstructure can be properly captured. On the microscale, the load–displacement response of cement paste is numerically simulated then experimentally validated. In order to rationally investigate the role of cement paste microstructure, the obtained load–displacement response was then formulated to several types of model inputs reflecting different degree of brittleness. These inputs were then used for simulating the mechanical response of macroscale cementitious lattices. By comparing the simulation to experiment, multi-linear behavior (ML) was found to an appropriate method to include the realistic pre-critical cracking and post-peak softening of cement paste in the model. Compared to ideally brittle behavior, using ML as input, the discrepancy between simulated and experimentally tested fracture energy decreases from 37.4% to 12.4%. In addition, the influence of lattice structure on the strength of cementitious lattices was also accurately captured by the proposed model. Randomized cementitious lattice has 21.6% (22.0% from simulation) lower strength than regular lattice. Moreover, the influence of fracture criterion of the proposed model is discussed and elaborated. Owning to the high simulation accuracy, the proposed multi-scale method in this work could be helpful for tailoring the fracture cementitious lattice materials for future studies.

Hysteresis response of rotary friction dampers developed for seismic operational performance of non-structural components vulnerable to overturning

The electrical facilities in buildings play important roles in maintaining operational performance during and after earthquakes. In this study, rotary friction dampers were developed for electrical facilities vulnerable to overturning, and cyclic loading tests were performed for the corresponding sub-assemblies (comprising friction plates), aiming to investigate the hysteresis response(s) of the friction dampers. The primary test parameters included the number of bolts used for fabricating the friction plates, torque applied to the bolts for their fixation to the friction plates, and cyclic loading frequency. In total, three series of 24 full-scale friction damper specimens were fabricated and tested according to the guidelines specified in the Korean seismic design standard (KDS 41 17, 2019). Based on the test results, the mechanical characteristics and seismic performance of the friction dampers were assessed and investigated in details. A macro-analytical model was developed to simulate the load–displacement response of the friction dampers, and its prediction showed a good correlation with the experimental results. Finally, dynamic analysis was performed by applying the developed friction damper to the entire system (mold transformer). As a result of the analysis, the response displacement of the detail with friction damper was reduced by about 95% in the X-direction and about 70% in the Y-direction compared to the displacement of the conventional detail.

Effects of gaps on the seismic performance of traditional timber frames with straight mortise-tenon joint: Experimental tests, energy dissipation mechanism and hysteretic model

The gaps are very common in the mortise-tenon (M-T) joints of the column-frame layer for the existing ancient timber buildings, which severely threaten the whole stability and safety of the structures. To study the effects of gaps on the seismic performance of traditional timber frames with straight M-T joint. Three 1/3.2-scaled straight M-T jointed timber frames, including one intact timber frame as a contrast and two timber frames with different gaps, were fabricated using Pinus sylvestris logs, and subjected them to reversed cyclic loading tests in strict accordance with the international test standard ISO-16670. The failure modes, load-displacement hysteretic response, strength, initial elastic stiffness, ductility, and stiffness degradation of the specimens were analyzed. The energy dissipation mechanisms of the timber frames with different gaps were evaluated, based on the law of energy conservation. Results indicated that the strength, initial elastic stiffness, and hysteretic energy dissipation capacity of the timber frames with gaps decreased significantly with increasing damaged degree. The gap can weaken the ductility of the timber frame, however, the inter-story drift ratio of the timber frame with gap can reached 0.16, indicating good deformation capacity. The gap had little effect on the degradation degree of the residual stiffness of the timber frame under large displacement amplitude. When the damage degree was 10%, under large displacement amplitude, the hysteretic energy consumption, elastic strain energy, and gravitational potential energy of the timber frame approximately accounted for 54%, 16%, and 30% of the total input energy, respectively. Based on the experimental results, the empirical formulas related to key cyclic performance parameters, considering the gap effects, were established. Based on the empirical relationships of the key hysteretic parameters of the timber frame with gaps, an improved hysteretic model for a timber frame with a gap was proposed and also validated. Good agreement between the model predictions and experimental results was observed.

Post-strengthening rapid repair of damaged RC columns using CFRP sheets for confinement and NSM-CFRP ropes for flexural strengthening

RC columns have been upgraded and strengthened with FRP confinement all around the globe. Future cases of repair will likely encounter RC columns that were strengthened previously with FRP confinement. However, studies on repairing damaged columns that were enhanced by confinement before damage are not currently available. Moreover, there is a vital need for an emergency repair technique that can be used to rapidly repair damaged columns of essential structures after a seismic event. In this study, the time required to complete the repair was a key factor to propose a rapid CFRP-based repair technique. A total of four specimens, each one consisted of two columns, were fabricated and tested. All parameters were kept the same except the difference in using CFRP between the control specimen and the strengthened and repaired specimens. The technique was applied to half-scale square RC columns subjected to combined axial and cyclic lateral loads. NSM-CFRP ropes were used for flexural strengthening and EB-CFRP sheets were used for lateral confinement. It was found that the repair technique was completed in three days. Test results showed that the proposed repair technique was effective not only by restoring the original strength, but also by improving the strength significantly. A strength improvement of at least 65% and a ductility ratio of at least 6.12 were observed. The measured and idealized load–displacement response showed that the ductility of the repaired column was reasonably acceptable. The proposed technique appears promising and may be considered as a permanent repair technique.

Mechanical Properties of Prismatic Li-Ion Batteries—Electrodes, Cells, and Stacks

Abstract Mechanical abusive loadings, as an inevitable consequence of road accidents, can damage the embedded energy storage system in an electric vehicle and deform its constitutive parts, e.g., the lithium-ion batteries. Therefore, to study the mechanical responses of these batteries and avoid expensive testing equipment and rigorous safety percussions, researchers are propelled toward utilizing numerical models. Computationally cost-efficient homogenized finite element models that represent the whole battery in the form of a uniform medium are the most feasible solution, especially in large-scale battery stacks simulations. Compared to the other form factors of the batteries, prismatic cells have been understudied even though they have higher packaging efficiency, by making optimal use of space. In this article, a comprehensive homogenization and failure calibration method was developed for these prismatic cells. The homogenization was done through extensive uniaxial components tests of the jellyroll and the shell casing. In addition, biaxial tensile tests and simulations were used to calibrate strain-based failure criteria for the components. The calibrated homogenized model is validated in various punch loading scenarios and used in the characterization of the load–displacement responses and failure modes of the stacked cell configurations. In the stacked simulations, due to the cushion-like behavior of the other cells, the failure happens in higher values of displacement compared to a single cell. However, the normalized intrusion percentages for the battery stacks are lower compared to a single battery cell. This emphasizes the importance of the safety assessment of an electric vehicle based on the failure analysis of the battery stacks rather than a single cell. This goal would be feasible through simulations of only homogenized cell models in the stacked configurations, which are elaborated in this article for prismatic cells.

Damage of prismatic lithium‐ion cells subject to bending: Test, model, and detection

AbstractThe mechanically induced internal short circuit (ISC) is one of the major safety concerns of lithium‐ion batteries. Mechanical abuse tests are often performed to evaluate the integrity and safety of lithium‐ion batteries under mechanical loadings. Except for the widely explored compression‐dominated indentation tests, bending is another typical real‐world loading condition that is tension‐dominated. To investigate the mechanical damage and ISC behavior of batteries under bending, we carried out controlled three‐point bending tests in four progressive steps on prismatic battery cells with maximum deflections ranging from 38% to 76% of the cell thickness. None of the tested cells experienced an ISC. We then conducted 3D X‐ray computed tomography (CT) scanning on the bent cells after unloading. X‐ray CT images showed three out of the four tested cells have extensive cracking in the electrode layers at the bottom side (opposite to the loading head). This indicates that cracking does not necessarily lead to an ISC under bending. Electrochemical impedance spectroscopy was also measured on the bent cells and substantial changes were observed. Both the bulk resistance and charge‐transfer resistance increased significantly after bending, which could influence the battery performance and lifespan. We then developed a detailed finite (FE) element model to further investigate the mechanical deformation and failure mechanisms. The FE model successfully predicts the load–displacement response and reproduces the deformation patterns. The findings and the FE model developed in the present study provide useful insights and tools for the battery structure and crash safety design.image

Temperature effect on the static mode I delamination behavior of aerospace‐grade composite laminates: Experimental and numerical study

AbstractAerospace structures are exposed to high‐temperature conditions during service. In‐depth study for the temperature effect on composite interlaminar properties is important for the structural design and reliable application. In this study, mode I delamination behaviors at different temperatures are investigated, to understand the effects of temperature on the delamination growth process, including fracture toughness, bridging stress, and failure mechanism. It is found that R‐curve behavior presents at all temperatures. The initial and steady‐state fracture toughnesses exhibit linear increase trends with the increase of the temperature, from which equations are established to predict the initial and steady‐state fracture toughnesses at other temperatures. More bridging fibers are observed at higher temperatures, and the resulted fracture resistance at 130°C is 136.9% higher than that at room temperature. The maximum bridging stress also increases with the increase of temperature. A numerical framework based on the cohesive zone model is established for delamination modeling. Material parameters at various temperatures are obtained by an exponential model. Suitable values of interfacial parameters in cohesive elements are numerically determined. Predicted load–displacement responses agree well with the experimental ones, illustrating the applicability of the proposed numerical method.

Anti-collapse performance of concrete-filled steel tubular composite frame with assembled tensile steel brace under middle column removal

To study the effect of assembled tensile steel brace on the progressive collapse resistance of concrete-filled steel tubular (CFST) structures, two 1/4-scaled two-bay two-story composite frames with CFST columns and profiled steel–concrete composite beams were tested pseudo-statically under a middle column removal scenario. The vertical load–displacement responses and failure modes of two specimens were analyzed. Especially, the effects of assembled tensile steel braces on the anti-collapse performance of the frames were discussed. Experimental results show that the assembled tensile steel braces delayed the failure of the upper beam and significantly improved the structural bearing capacity and ductility of the frame. The horizontal reaction forces of the specimens are compressive forces due to the compressive arch action in the initial loading stage, and they change from compression to tension due to the catenary action. Numerical parametric analysis indicates that the splint bolt connection configuration can effectively improve the bearing capacity of the frame models by increasing the bolt preload and friction coefficient. Furthermore, the collapse resistance of the structure is calculated based on the simplified elastic theory method, considering the effect of the steel braces. It is believed that the assembled tensile brace between CFST columns could be used as a reinforcement method to improve the collapse resistance of the framed structure.

Plastic hinge regions of prefabricated concrete columns with grouted sleeves and simplified calculation method for plastic hinge length

To design prefabricated concrete columns with grouted sleeves (PCC-GSs), the development and damage process of the plastic hinge (PH) regions for the PCC-GSs need to be clarified. In this study, a finite element analysis (FEA) method for the PCC-GSs was verified through experimental results, including the failure modes, load–displacement responses, and physical plastic hinge lengths (PHLs). Consequently, a series of finite element models (FEMs) were constructed. The effects of parameters such as grouted sleeve (GS) height, axial force ratio, and shear span ratio on the PHL for the PCC-GSs were systematically analysed under cyclic loading. Finally, with the discussion of the existing empirical models for the equivalent PHL (Lp), a simplified calculation model of Lp for PCC-GSs was proposed and evaluated. The results indicate the following. (1) The PH of PCC-GSs may move up or down, and its PH development mode is significantly different from that of the CIP RC column. (2) The axial force ratio n, shear span ratio z/d, longitudinal reinforcement ratio ρs, rebar yield strength fy, and GS height LGS all have a significant influence on the PH region of PCC-GSs, especially LGS. (3) The proposed model is more suitable to calculate the PHL for PCC-GSs with considering the effects of LGS, n, z/d, ρs, fy.

Energy-Based Approach: Analysis of a Vertically Loaded Pile in Multi-Layered Non-Linear Soil Strata

Numerous studies have been reported in the published literature on analytical solutions for a vertically loaded pile installed in a homogeneous single soil layer. However, piles are rarely installed in an ideal homogeneous single soil layer. This study presents an analytical model based on the energy-based approach to obtain displacements in an axially loaded pile embedded in multi-layered soil considering soil non-linearity. The developed analytical model incorporating Euler-Bernoulli beam theory proved to be an effective way in estimating the load-displacement responses of piles embedded in multi-layered non-linear elastic soil strata. The differential equations are solved analytically and numerically using the variational principle of mechanics. A parametric study investigated the effect of explicit incorporation of soil properties and layering in order to understand the importance of predicting appropriate pile displacement responses in linear elastic soil system. It is clear from the results that the analyses which consider the soil as a single homogeneous layer will not be able to produce an accurate estimation of the pile stiffnesses. Therefore, it is highly important to account for the effect of soil layering and the non-linear response. The pile displacement response is obtained using the software MATLAB R2019a and the results from the energy-based method are compared with those obtained from the field test data as well as the Finite Element Analysis (FEA) based on the software ANSYS 2019R3. The non-linear elastic constitutive relationship which described the variation of secant shear modulus with strain through a power law has shown reasonably accurate predictions when compared to the published field test data and the FEA. The developed mathematical framework is also more computationally efficient than the three-dimensional (3D) FEA.