Axial Compressive Force Research Articles

Experimental study on the cyclic performance of innovative self-centering three-dimensional isolation bearing

To improve vertical seismic isolation and seismic resilience in isolation bearings, this paper introduces an innovative three-dimensional isolation bearing combining a disc-spring system (DSS), a high-damping rubber bearing (HDR), and a horizontal spring system (HSS). The DSS is designed with low vertical stiffness to enhance vertical isolation, while the HSS provides self-centering force to improve the seismic resilience of the HDR. This study first presents a comprehensive theoretical analysis of the horizontal and vertical stiffness composition. The vertical performance of this three-dimensional isolation bearing is attributed to the DSS, while the HSS and HDR jointly contribute to its horizontal performance. Seven specimens were designed and subjected to shear-compression cyclic tests to assess the horizontal and vertical cyclic performance. Experimental parameters included loading amplitude, loading frequency, vertical pre-load, and DSS combinations for vertical tests, and axial compression force, loading frequency, shear strain, and HSS function in horizontal tests. The cyclic performance parameters for the three-dimensional isolation bearing, including equivalent damping ratio, equivalent stiffness, and energy dissipation, was evaluated. In general, the proposed three-dimensional isolation bearing exhibits stable cyclic performance and advantageous seismic resilience, warranting its promotion to practical engineering applications.

Seismic Performance of Pile Groups under Liquefaction-Induced Lateral Spreading: Insights from Advanced Numerical Modeling

Post-earthquake investigations have shown that piles in liquefiable soils are highly susceptible to damage, especially in sloping sites. This study examines the seismic performance of pile groups with lateral spreading through advanced numerical modeling. A three-dimensional finite element model, validated against large-scale shaking table test results, is implemented to capture the key mechanisms driving the dynamic response of pile groups under both inertial and kinematic loading conditions. Parametric seismic response analyses are conducted to compare the behavior of batter and vertical piles under varying ground motion intensities. The results indicate that batter piles experience increased axial compressive and tensile forces compared to vertical piles, up to 70% and 20%, respectively. However, batter piles provide enhanced lateral stiffness and shear resistance compared to vertical piles, reducing horizontal displacements by up to 20% and tilting the cap by 85% under strong ground motion. The results demonstrate that batter piles not only enhance the overall seismic stability of the structure but also mitigate the risk of liquefaction-induced lateral spreading in the near-field through pile-pinning effects. While vertical piles are more commonly used in practice, the distinct advantages of batter piles for seismic stability highlighted in this study may encourage using more advanced numerical modeling in engineering projects.

Effects of stiffeners on anchor rod flexural strength in column base-plate connections

The present paper reports results of a numerical investigation of the mechanical behavior of a column base plate connection subjected to an axial compression force and a bending moment. A three-dimensional nonlinear model was developed, using the Cast3M software, and validated against experimental data. In addition, the material nonlinearity as well as contact conditions between the different components of the connection were thoughtfully considered. Based on the validated model, an extensive parametric analysis was conducted to investigate the effect of stiffeners on the forces in the anchor rods. The results clearly indicate that the design approaches that consider only the tensile strength of anchor rods while neglecting the bending moments can lead to a poor estimation of the forces applied to these rods. They also suggest that adding stiffeners provides additional strength and reduces the anchor rod bending in one direction. However, it is important to note that the stiffeners also induce an additional moment in the opposite direction. This could make the anchor rod more susceptible to biaxial bending with tension. Furthermore, this study proposes a new specific shape of stiffener is suggested (cbp5). It was concluded that the proposed shape of stiffeners allows a more uniform distribution of forces and avoids excessive stress concentrations, effectively prevents the biaxial bending in the anchor rod.

The effects of setup parameters on the measured kinetic output of cervical disc prostheses

Mechanical testing machines are used to evaluate kinematics, kinetics, wear, and efficacy of spinal implants. The simulation of "physiological" spinal loading conditions necessitates the simultaneous use of multiple actuators. The challenge in achieving a desired loading profile lies in achieving close synchronization of these actuators. Errors in load application can be attributed to both the control system and the intrinsic sample response. Moreover, the presence of friction in the setup can have an impact on the measured outcome. The optimization of setup parameters can substantially improve the ability to simulate spinal loading conditions and obtain reliable data on implant performance. In this study, a reproducible kinematic test protocol was developed to evaluate the sensitivity of the kinetic response (i.e., measured loads, moments, and stiffnesses) of a cervical disc prosthesis to several testing parameters. In this context, five ceramic ball and socket sample implants were mounted in a 6 DOF material testing machine and tested with a constant axial compressive force of 100 N in two motion modes: 1) flexion-extension (±7.5°) and 2) lateral bending (±6°). Parameters including rotation rate, slider friction, friction between the samples' articulating surfaces, and moment arm were considered to determine their effects on measured kinetic parameters. The sensitivity analysis indicated that all setup parameters except friction between the samples' articulating surfaces had a substantial effect on the results. The findings were then compared to predictions from a free body diagram to determine the optimal setup parameters. Consequently, the setup with the lowest rotation rate and employing passive sliders yielded results that were consistent with the free body diagram. This study demonstrated the significance of a comprehensive setup evaluation for reliable and reproducible testing of spinal implants, also for comparison between labs.

Evaluation of Load on Cervical Disc Prosthesis by Imposing Complex Motion: Multiplanar Motion and Combined Rotational-Translational Motion.

(1) Background: The kinematic characteristics of disc prosthesis undergoing complex motion are not well understood. Therefore, examining complex motion may provide an improved understanding of the post-operative behavior of spinal implants. (2) Methods: The aim of this study was to develop kinematic tests that simulate multiplanar motion and combined rotational-translational motion in a disc prosthesis. In this context, five generic zirconia-toughened alumina (BIOLOX®delta, CeramTec, Germany) ball and socket samples were tested in a 6 DOF spine simulator under displacement control with an axial compressive force of 100 N in five motion modes: (1) flexion-extension (FE = ± 7.5°), (2) lateral bending (LB = ± 6°), (3) combined FE-LB (4) combined FE and anteroposterior translation (AP = 3 mm), and (5) combined LB and lateral motion (3 mm). For combined rotational-translational motion, two scenarios were analyzed: excessive translational movement after sample rotation (scenario 1) and excessive translational movement during rotation (scenario 2). (3) Results: For combined FE-LB, the resultant forces and moments were higher compared to the unidirectional motion modes. For combined rotational-translational motion (scenario 1), subluxation occurred at FE = 7.5° with an incremental increase in AP translation = 1.49 ± 0.18 mm, and LB = 6° with an incremental increase of lateral translation = 2.22 ± 0.16 mm. At the subluxation point, the incremental increase in AP force and lateral force were 30.4 ± 3.14 N and 40.8 ± 2.56 N in FE and LB, respectively, compared to the forces at the same angles during unidirectional motion. For scenario 2, subluxation occurred at FE = 4.93° with an incremental increase in AP translation = 1.75 mm, and LB = 4.52° with an incremental increase in lateral translation = 1.99 mm. At the subluxation point, the incremental increase in AP force and lateral force were 39.17 N and 38.94 N in FE and LB, respectively, compared to the forces in the same angles during the unidirectional motion. (4) Conclusions: The new test protocols improved the understanding of in vivo-like behavior from in vitro testing. Simultaneous translation-rotation motion was shown to provoke subluxation at lower motion extents. Following further validation of the proposed complex motion testing, these new methods can be applied future development and characterization of spinal motion-preserving implants.

Machine-learning assisted analysis on the seismic performance of steel reinforced concrete composite columns

This paper presents the data-driven analysis on the seismic performance of steel reinforced concrete (SRC) composite columns by using machine learning (ML) algorithms. A total of 248 test data of SRC columns subjected to the combined axial compressive force and low reversed cyclic horizontal force was collected from the published literatures to form the database. Since the seismic action triggers the SRC columns to suffer from different failure mode and hence exhibit quite different load bearing mechanism, six ML algorithms were employed to facilitate the failure mode classification and bearing capacity prediction. It was found that the Random Forest (RF) model predicts the failure mode most accurately, while XGBoost model delivers the best estimation of bearing capacity. To further evaluate the feasibility of ML models and unveil the interaction between different variables, interpretability analysis of ML models was carried out. In comparison with the conventional empirical judgement and theoretical derivation, ML model delivers enhanced accuracy and robustness to predict the seismic performance of SRC columns, and hence it could be used as a promising alternative for the preliminary design and analysis of SRC columns.

Flexural behaviour of shallow-embedded steel column bases

This paper investigated the flexural behaviour (the initial rotational stiffness and ultimate moment resistance, in particular) of the shallow-embedded column bases through experimental and numerical approaches. Three full-scale tests with different embedded depth ratios (i.e., 0.5, 1.0 and 1.5) were carried out, from which the moment-resisting mechanisms were identified and the effects of the embedded depth ratio on the initial stiffness, moment resistance and ductility were evaluated. The test results were further used to evaluate the accuracy of the available resistance and stiffness models for the shallow-embedded column bases. The resistance models codified in design codes GB 50017-2017 and AISC 341-16 are highly conservative, with an average prediction accuracy of 0.268 and 0.451, respectively; by contrast, the resistance models recently reported in the published articles show better accuracy. The stiffness models are fewer in number and are also inaccurate for the shallow-embedded column bases. Complementary finite-element models were developed and validated. Subsequently, systematic parametric finite-element analyses were performed to investigate the effects of axial force and shear force in the steel column, as well as those of the structural details such as the presence of base plate, arrangement of anchor bolts and width of concrete foundation. Shear force has an adverse effect on both the initial stiffness and moment resistance, and this effect becomes more significant with the increase in the embedded depth ratio; axial compression force leads to an increase in both the initial stiffness and moment resistance, which is more pronounced for embedded column bases with smaller η-values. Among all structural details, the presence of the base plate has the most notable influence on the flexural behaviour of the shallow-embedded column base, increasing both its initial stiffness and moment resistance; comparatively, the effects of the other structural details are minor or even could be ignored.

Numerical Study on the Mechanical Performance of a Flexible Arch Composite Bridge with Steel Truss Beams over Its Entire Lifespan

Steel truss–arch composite bridge systems are widely used in bridge engineering to provide sufficient space for double lanes. However, a lack of research exists on their mechanical performance throughout their lifespan, resulting in uncertainties regarding bearing capacity and the risk of bridge failure. This paper conducts a numerical study of the structural mechanical performance of a flexible arch composite bridge with steel truss beams throughout its lifespan to determine the critical components and their mechanical behavior. Critical vehicle loads are used to assess the bridge’s mechanical performance. The results show that the mechanical performance of the bridge changes significantly when the temporary piers and the bridge deck pavement are removed, substantially influencing the effects of the vehicle loads on the service life. The compressive axial force of the diagonal bar significantly increases to 33,101 kN near the supports during the two construction stages, and the axial force in the upper chord of the midspan increases by 4.1 times under a critical load. Moreover, the suspender tensions and maximum vertical displacement are probably larger than the limit of this bridge system in the service stage, and this is caused by the insufficient longitudinal bending stiffness of truss beams. Therefore, monitoring and inspection of critical members are necessary during the removal of temporary piers and bridge deck paving, and an appropriate design in steel truss beams is required to improve the life cycle assessment of this bridge system.

An Extended Neck Position is Likely to Produce Cervical Spine Injuries Through Buckling in Accidental Head-First Impacts During Rugby Tackling

Catastrophic cervical spine injuries in rugby often occur during tackling. The underlying mechanisms leading to these injuries remain unclear, with neck hyperflexion and buckling both proposed as the causative factor in the injury prevention literature. The aim of this study was to evaluate the effect of pre-impact head–neck posture on intervertebral neck loads and motions during a head-first rugby tackle. Using a validated, subject-specific musculoskeletal model of a rugby player, and computer simulations driven by in vivo and in vitro data, we examined the dynamic response of the cervical spine under such impact conditions. The simulations demonstrated that the initial head–neck sagittal-plane posture affected intervertebral loads and kinematics, with an extended neck resulting in buckling and supraphysiologic intervertebral shear and flexion loads and motions, typical of bilateral facet dislocation injuries. In contrast, an initially flexed neck increased axial compression forces and flexion angles without exceeding intervertebral physiological limits. These findings provide objective evidence that can inform injury prevention strategies or rugby law changes to improve the safety of the game of rugby.

Atypical lesional association (Talus Fracture + Pilon Fracture): A case report

Background: Talus fractures represent 3% to 6% of all foot and ankle fractures and are frequently associated with significant morbidity and poor outcomes. They typically result from high-energy trauma, such as motor vehicle accidents or falls from heights. The combination of talar body and tibial plafond fractures is particularly rare, with few cases reported in the literature. Case Report: We present the case of a 20-year-old female who sustained a closed injury to her right ankle after a 6-meter fall. Clinical examination revealed swelling, pain, and bruising without skin opening or neurovascular disturbances. Radiographs and a CT scan identified a non-displaced fracture of the tibial plafond, a medial malleolus fracture, and a posterior process talus fracture. The patient underwent closed reduction and internal fixation with percutaneous screws. At six months post-surgery, she exhibited a good functional outcome with minimal residual pain and slight limitations in ankle movement. Discussion: Talar body fractures commonly result from falls that exert axial compression or shearing forces. Severe cases involve comminution of the ankle and subtalar joints, often accompanied by malleoli fractures. The concomitant fracture of the tibial plafond and talus, as seen in this case, is rare. Managing such injuries is challenging due to high risks of avascular necrosis, subtalar arthritis, and restricted ankle motion. Thorough radiographic and clinical assessments are crucial for effective management, emphasizing the need for careful preoperative planning, precise anatomical reduction, and stable fixation. Conclusion: This rare case of combined talus body and tibial plafond fractures highlights the importance of comprehensive evaluation and appropriate management to minimize serious complications.

Optimization of Hanger Spacing of Steel Arch Bridges Using Dynamic Loads

Bridges are basic infrastructure that must be met to create regional connectivity in Indonesia. One type of bridge that is often used is a curved bridge, which has the advantages of high strength, attractiveness, aesthetics and economy. In order to accelerate the development of bridge infrastructure, an efficient innovation in curved bridge design is needed. The development of curved bridge structures to achieve efficient designs has received much attention in several decades. However, researchers have only focused on optimising the geometry variation of the arch height. Therefore, the aim of this research is to innovate the optimisation of the hanger spacing on the arch bridge structure. In order to obtain optimal results, a bridge model is carried out by varying the hanger spacing of the centre model with a hanger spacing ratio of (1.3 - 1.1 - 0.9 - 0.7), a flat model with a hanger spacing ratio of (1 - 1 - 1 - 1) and an edge model with a hanger spacing ratio of (0.7 - 0.9 - 1.1 - 1.3), so that from the three models, the effect of hanger location on three conditions is obtained. Each model is modelled in the SAP2000 software and given a bridge service load to obtain the internal forces and deflections that occur. The output of the internal force and deflection is then analysed to determine the effect of the location of the bridge service hanger. The serviceability of the bridge is also analysed by calculating the ratio between the weight of the bridge and the deflection that occurs. The results of the analysis show that the location of the hanger affects the performance of the arch bridge structure. The centre model bridge design produces the most efficient structural performance in resisting the compressive axial forces and moments that occur, and produces the least deflection. Meanwhile, the edge model will provide the most efficient structural performance in resisting tensile axial forces. By referring to the results of the bridge weight to deflection ratio analysis, it can be concluded that the centre model produces the most efficient structural design when compared to other curved bridge models.

Kinematics, kinetics, and new insights from a contemporary analysis of the first experiments to produce cervical facet dislocations in the laboratory.

The first experimental study to produce cervical facet dislocation (CFD) in cadaver specimens captured the vertebral motions and axial forces that are important for understanding the injury mechanics. However, these data were not reported in the original manuscript, nor been presented in the limited subsequent studies of experimental CFD. Therefore, the aim of this study was to re-examine the analog data from the first experimental study to determine the local and global spinal motions, and applied axial force, at and preceding CFD. In the original study, quasistatic axial loading was applied to 14 cervical spines by compressing them between two metal plates. Specimens were fixed caudally via a steel spindle positioned within the spinal canal and a bone pin through the inferior-most vertebral body. Global rotation of the occiput was restricted but its anterior translation was unconstrained. The instant of CFD was identified on sagittal cineradiograph films (N = 10), from which global and intervertebral kinematics were also calculated. Corresponding axial force data (N = 6) were extracted, and peak force and force at the instant of injury were determined. CFD occurred in eight specimens, with an intervertebral flexion angle of 34.8 ± 5.6 degrees, and a 3.1 ± 1.9 mm increase in anterior translation, at the injured level. For seven specimens, CFD was produced at the level of transition from upper neck lordosis to lower neck kyphosis. Five specimens with force data underwent CFD at 545 ± 147 N, preceded by a peak axial force (755 ± 233 N) that appeared to coincide with either fracture or soft tissue failure. Re-examining this rich dataset has provided quantitative evidence that small axial compression forces, combined with anterior eccentricity and upper neck extension, can cause flexion and shear in the lower neck, leading to soft tissue rupture and CFD.

Limit state equation and failure pressure prediction model of pipeline with complex loading

Assessing failure pressure is critical in determining pipeline integrity. Current research primarily concerns the buckling performance of pressurized pipelines subjected to a bending load or axial compression force, with some also looking at the failure pressure of corroded pipelines. However, there is currently a lack of limit state models for pressurized pipelines with bending moments and axial forces. In this study, based on the unified yield criterion, we propose a limit state equation for steel pipes under various loads. The most common operating loads on buried pipelines are bending moment, internal pressure, and axial force. The proposed limit state equation for intact pipelines is based on a three-dimensional pipeline stress model with complex load coupling. Using failure data, we investigate the applicability of various yield criteria in assessing the failure pressure of pipelines with complex loads. We show that the evaluation model can be effectively used as a theoretical solution for assessing the failure pressure in such circumstances and for selecting appropriate yield criteria based on load condition differences.

Post-buckling behavior of variable-arc-length elastica pipe conveying fluid including effects of self-weight and pressure variation

This paper investigated the post-buckling behaviors of a variable-arc-length (VAL) elastica pipe caused by internal transporting fluid motion, accounting for the effects of the self-weight and variation of internal fluid pressure. Both weak-form and strong-form formulations of the VAL elastica pipe were developed. The weak-form formulation was derived by the virtual work principle, and later solved using the nonlinear finite element method (FEM). The strong-form formulation was derived using equilibrium of the force and moment equations, the geometrical relationship of the differential pipe segment, and the energy conservation of the transported fluid. Because of the large displacement analysis, the variation in the internal pressure inside the pipe was considered, which was taken into account by energy conservation based on the Bernoulli principle. Then, the set of nonlinear governing first-order differential equations, corresponding to the two-point boundary value problem, was conveniently solved using the shooting optimization method (SOM). The numerical results obtained from the presented FEM and SOM analyses independently verified each other, with good agreement between these two methods. The parametric study considered the effects of gravity load (pipe and fluid self-weights) and internal fluid pressure on the post-buckling characteristics of the VAL pipe. The numerical results showed that without the pipe and internal fluid weights, the transporting fluid exerted an axial compressive force on the pipe, causing post-buckling phenomena. Beyond the critical state, the support rotation and the length of the VAL pipe increased as the internal fluid velocity decreased. Finally, by including the effect of self-weight, the mode exchange of the odd buckling modes (1st and 3rd modes) was found from the load-displacement path.

Finite element analysis of locally strengthened stainless-steel tube under lateral impact loading

In this study, a Finite Element (FE) model of locally strengthened high-strength stainless-steel tube subjected to lateral impact loads is established using LS-DYNA to investigate its dynamic behaviours. The accuracy of the FE results is verified by comparing with the test results. The impact force, bending moment, stress and strain responses as well as the internal energy dissipation histories of the strengthened tube are analysed during the entire impact process. The results indicate that the impact resistance of the strengthened tube is obviously enhanced as compared to hollow stainless-steel tube. Furthermore, parametric studies are conducted to reveal the influence of axial compressive force, impact position, impact velocity and material strength on the impact behaviour of the strengthened tube. The results show that the application of axial compressive force reduced the impact force and increased the deformations of the strengthened tube. The impact resistance of the strengthened tube performed an increasing trend when moving the impact position towards the support and increasing the material strength. In addition, the increase of impact velocity significantly reduced the impact duration. Finally, design recommendations and process were proposed to facilitate the application of locally strengthened tube.

Geo-mechanical and geo-morphology characterisation of the cap rocks in the Niger Delta for potential carbon capture and storage

The world has been battling climate change which is caused by an excessive amount of carbon dioxide in the atmosphere. Carbon sequestration in geological sinks was identified as one of the major methods to curb and reduce the amount of carbon dioxide in the atmosphere. The carbon dioxide stored in the geological formations must not escape back into the atmosphere. Characterisation of potential reservoirs for geological sequestration is pertinent for injectivity, capacity, and most importantly containment of carbon dioxide. The cap rock is one of the most important factors determining carbon sequestration success. This study focuses on the preliminary characterisation of the caprocks for evaluating potential subsurface storage of carbon dioxide based on their petrophysical characteristics. X-ray Diffraction and X-ray Fluorescence provided the mineralogical composition and geochemical data of the cap rocks while Scanning Electron Microscopy-EDS was used to identify the qualitative information on the micromorphological textural structure of the cap rocks in the Niger Delta. Conventional Triaxial experiments were used to determine the elastic and geo-mechanical strength of the caprocks. It was identified that the grain skeleton of caprocks in the region is predominated by Quartz, Albite, and Muscovite. The ratio of the tectosilicate and phyllosilicate minerals indicates that the cap rocks are silicate shale. The peak strength of the caprocks ranged from 48.85 to 80.50 MPa and are classified as strong rocks. The cap rocks showed a quasi-elastic behaviour after being subjected to compressive axial force. The elastic modulus of the caprocks was also observed. The characteristics exhibited by the shale caprock at the rock matrix level are highly favourable for sealing carbon dioxide and hence indicate capability for use in carbon sequestration.

Finite element analysis for free vibration of pipes conveying fluids–physical significance of complex mode shapes

A finite element formulation is presented for the natural vibration analysis of pipes conveying fluids. The solution of the resulting quadratic eigenvalue problem generally yields complex eigenvalues and eigenvectors. The present study then develops a robust mathematical procedure that combines the real and imaginary components of the eigenvectors to form physically attainable (i.e., real) mode shapes. The procedure yields a family of solutions that is more general than previously known solutions. The well-known classical mode shape is shown to be recoverable as a special case from the present solution. The study provides new insights on the effects of viscous damping, axial compressive force, and the flexibility of intermediate pipe supports on the response. Additionally, the study develops a novel algorithm based on Hermitian angles between eigenvectors to automate the tracing of mode evolution in the frequency-velocity plots.

РЕКОМЕНДАЦИИ ДЛЯ МОДЕЛИРОВАНИЯ ЭЛЕМЕНТОВ ИЗ СТАЛЬНЫХ ТОНКОСТЕННЫХ ПРОФИЛЕЙ

Despite the increase in the growth rate of construction with the use of steel thin-walled sections, the building code for the design and calculation of these structures has a number of conventions and indicates the preferred use of the results of experimental studies in the design. Fullscale tests are generally not available during design, so numerical modelling is a correct alternative. The analysis of existing scientific literature shows that there is no consensus among researchers regarding the main parameters of the models and the modelling algorithm in general, so the aim of the paper is to develop recommendations for modelling thin-walled sections. The results of the study for object made from a coupled sigma profile under axial compressive force conditions let us develop key recommendations for modelling including the use of finite element type, finite element mesh parameters, the mechanism of application of boundary conditions, external loads and other model parameters. The results were verified by analytical methods of thin-walled sections calculation. The obtained convergence of the results indicates the possibility of using these recommendations in the design and calculation of thin-walled structures.

Effects of prestress in the coating of an elastic disk

An elastic disk is coated with an elastic rod, uniformly prestressed with a tensile or compressive axial force. The prestress state is assumed to be induced by three different models of external radial load or by ‘shrink-fit’ forcing the coating onto the disk. The prestressed coating/disk system, when loaded with an additional and arbitrary incremental external load, experiences incremental displacement, strain, and stress, which are solved via complex potentials. The analysis incorporates models for both perfect and imperfect bonding at the coating/disk interface. The derived solution highlights the significant influence not only of the prestress but also of the method employed to generate it. These two factors lead, in different ways, to a loss or an increase in incremental stiffness for compressive or tensile prestress. The first bifurcation load of the structure (which differs for different prestress generations) is determined in a perturbative way. The results emphasize the importance of modelling the load and may find applications in flexible electronics and robot arms subject to pressure or uniformly-distributed radial forces.

Analytical solution of pipeline upheaval buckling considering bi-linear axial pipe-soil interaction model

Under thermal loading, upheaval buckling of subsea pipelines occurs when the axial compressive force exceeds the critical buckling load. In order to accurately predict the upheaval buckling behaviour of subsea pipelines, the axial pipe-soil resistance should be considered more precisely, rather than traditionally treated as rigid-plastic in prior analytical researches on pipeline upheaval buckling. Consequently, this study integrates a bi-linear axial pipe-soil resistance model into the mathematical framework of upheaval buckling. This mathematical model incorporates the von-Kármán type of geometrical nonlinearity and the Euler-Bernoulli beam theory. The research examines typical upheaval buckling behaviour and investigates the influence of axial mobilization distance and ultimate resistance on pipeline upheaval buckling behaviour. The results reveal that incorporating bi-linear axial pipe-soil resistance, in contrast to rigid-plastic resistance, leads the pipeline more susceptible to buckling. Displacement amplitudes increase with the axial mobilization distance during the post-buckling stage. Notably, a larger axial mobilization distance exerts a stronger influence on pipeline buckling. Moreover, the critical buckling temperature exhibits an almost linear negative correlation with axial mobilization distance and a positive correlation with axial ultimate resistance. Additionally, greater axial ultimate resistance magnifies the impact of axial mobilization distance. Therefore, in pipeline buckling design, it is advisable to consider a more sophisticated axial pipe-soil model to accurately account for these complexities.