Finite Element Program Research Articles

Stochastic model describing evolution of microstructural parameters during hot rolling of steel plates and strips

Enhancing strength-ductility synergy of materials has been for decades an objective of research on structural metallic materials. It has been shown by many researchers that significant improvement of this synergy can be obtained by tailoring heterogeneous multiphase microstructures. Since large gradients of properties in these microstructures cause a decrease of the local fracture resistance, the objective of research is to obtain smoother gradients of properties by control of the manufacturing process. Advanced material models are needed to design such microstructures with smooth gradients. These models should supply information about distributions of various microstructural features, instead of their average values. Models based on stochastic internal variables meet this requirement. Our objective was to account for the random character of the recrystallization and to transfer this randomness into equations describing the evolution of dislocations and grain size during hot deformation and during interpass times. The idea of this stochastic model is described in the paper. Experiments composed of uniaxial compression tests were performed to supply data for the identification and verification of the model in the hot deformation and static recrystallization parts. Histograms of the grain size were measured after hot deformation and at different times after the end of deformation. Identification and validation of the model were performed. The validated model, which predicts evolution of heterogeneous multiphase microstructure, is the main output of our work. The model was implemented in the finite element program for hot rolling of plates and sheets and simulations of these processes were performed. The model’s capability to compare and evaluate various rolling strategies are demonstrated in the paper.

Efficient numerical analyses of RC beams subjected to impact loading using axial-flexure-shear fiber beam model

Similar to wind and seismic loading, impact loading induced by e.g. vessel or vehicle collisions is another type of extreme loading that has become one of the major hazards for the safety of our infrastructural systems such as bridges and buildings. The development of effective strategies which can realistically quantify structural responses under impact loading becomes increasingly important. The widely-used finite-element (FE) simulations using general-purpose FE programs often require excessively high computational cost. This paper therefore aims to develop and implement a computationally efficient axial-flexure-shear fiber beam model based on Timoshenko beam theory with consideration of material non-linearity for the analyses of reinforced concrete (RC) beams under impact loading. The axial, flexural and shear deformation of RC sections during impact are effectively coupled at the fiber and material level. Numerical accuracy of the proposed fiber beam model for non-linear dynamic impact analyses is verified using experimental data from 15 sets of drop-hammer impact tests on scaled RC beams, including flexure-dominant slender beams and shear-dominant deep beams, which demonstrate the great advantage of the proposed fiber beam model over the classical Euler–Bernoulli fiber beam model for applications to impact scenarios where shear deformation of RC members becomes non-negligible.

Finite element analysis of RC buildings subjected to blast loading

In this paper, the response of reinforced concrete buildings subjected to blast loading under variable mass of TNT and different statical system will be discussed. The study was carried out using the finite element program (ABAQUS) by using two different models (Flat slab system and Solid slab system). The plastic behavior of steel reinforced bars and concrete has been incorporated through Johnson-cook model and concrete damage plasticity model respectively. The results obtained from the two models are in terms of Von-Mises stresses, deflection and concrete damage against varying mass of TNT. The results indicate that using double reinforced mesh has great influence on reinforced concrete slabs to withstand blast loads and the damage in concrete happened under blast loads in flat slab system where in columns while the damage happened under blast loads in solid slab system where in beams so it is recommended to use the solid slab system.

Behavior of CFRP-strengthened RC beams with circular web openings in shear zones: Numerical study

In practice, especially the basement floor beams are drilled and damaged by the users. In some cases, this damage to the beams can be significant for the load-bearing element and the whole structure. In this study, the behavior of reinforced concrete beams with circular openings and the failure types resulting from strengthening these beams with CFRP are parametrically investigated. The diameter of the opening/beam height ratio (D/H), concrete compressive strength, stirrup spacing, the position of the opening to the beam support, the type of CFRP application, CFRP ply orientation, and the number of CFRP layers were selected as parameters. Numerical models were verified using 9 specimens having different circular openings with/without CFRP strengthening and the analyses of 95 numerical models with the selected parameters were carried out utilizing the finite element program, ABAQUS. The ultimate load capacity, ductility, stiffness, energy dissipation capacity and failure modes of the beams were determined. As a result of the study, it was observed that there was no significant loss in ductility for the beams with D/H ≤ 0.3 and the number of CFRP layer and type of application did not have a significant effect on D/H ≤ 0.44. However, for the beams with D/H > 0.64, the CFRP application that completely surrounds openings should be preferred instead of partial CFRP strengthening. In addition, the concrete strength is an effective parameter for the beams with D/H ≤ 0.44. The effect of the stirrup spacings in the beam on the ductile behavior was also limited with the increase in the hole diameter. The number of CFRP layers should theoretically be 4 for an effective strengthening in beams with D/H > 0.44. Finally, U wrapping is recommended instead of using full wrapping. It has been seen that the location and diameter of the hole are very important parameters in the failure type of the beam.

Study on Sunshine Stress Effect of Long-Span and Wide Concrete Box Girder

In order to further clarify the sunshine stress effect of long-span and wide concrete box girder, the study selected a concrete box girder with 4 × 42 m span and 33.5 m width, formed the temperature field load through a field test and numerical simulation, established a numerical analysis model by using the finite element program of ANSYS, and comprehensively analyzed the longitudinal temperature stress distribution of a long-span and wide concrete box girder under sunshine. The midspan section of the first span of the box girder is selected for field stress measure, and the field measure results and numerical analysis results are compared and analyzed. The research shows that the results of field measurement and numerical simulation are basically consistent. Sunshine temperature has a great influence on long-span and wide concrete box girder, which should be paid enough attention.

An implicit integration algorithm based on invariants for isotropic elasto‐plastic models of the Cosserat continuum

AbstractA Finite Element (FE) procedure based on a fully implicit backward Euler predictor/corrector scheme for the Cosserat continuum is here presented. The integration algorithm is suitable for yield and plastic potential surfaces with general shape in the deviatoric plane. The key element of the integration scheme is the spectral decomposition of the stress tensor, which is achieved, despite the lack of symmetry, because of the mathematical structure of the yield function and the set of invariants chosen as independent variables. It is also shown that the choice of invariants enables considerable mathematical simplifications, which result in the reduction of the system of equations and unknowns of the elasto‐plastic problem from 19 to 1, and to rigorously handle the discontinuity at the apex of the surfaces. The algorithm has been implemented in a proprietary FE programme, and used for the constitutive model recently proposed by the same authors in this journal for the Cosserat continuum, which allows to set various classical failure criteria as yield and plastic potential surfaces. Numerical analyses have been conducted to simulate a biaxial compression test and a shallow strip footing resting on a Tresca, Mohr–Coulomb, Matsuoka–Nakai and Lade–Duncan soil. The benefits of the Cosserat continuum over the Cauchy/Maxwell medium are discussed considering mesh refinement, non‐associated flow and softening behaviour.

Three dimensional analyses of geocell reinforced encased stone column supported embankments on lithomargic clay

ABSTRACT Geocells are a superior form of reinforcement due to their cost-effectiveness and three-dimensional confining properties. However, numerical modeling of geocell is always challenging due to its three-dimensional honeycomb structure. The limitations of the equivalent composite approach (ECA) led to the recent development of full 3D numerical models, which consider geocell-infill material interaction. This paper discusses the time-dependent performance of geocell-reinforced encased stone column-supported embankment considering the actual 3D nature of geocells using the finite element program ABAQUS. Parametric studies were carried out to study the stress transfer mechanism, vertical deformation of the foundation soil, and stress-strain variation inside the geocell pockets. It is found from the analyses that with the provision of a geocell layer on top of Geosynthetic Encased Stone Columns (GESC), the stress concentration ratio improved by 47% at the end of consolidation compared to GESC alone. Also, an 80% reduction in foundation surface settlement is observed with geocell-sand mattresses. The geocell-sand mattress decreased the bulging of the stone columns, and almost 80% of the stone column bulging occurred by the end of the embankment construction. The proposed model’s numerical results show that the equivalent composite approach overestimated the stress concentration ratio and bearing capacity. The tensile stresses are non-uniformly distributed in the geocell pockets, and the maximum tensile force was mobilised at the geocell mid-height. Among the various geocell infill materials analysed, the aggregates were best suited considering the stress concentration ratio and vertical settlement. The numerical results supported the idea that encased stone columns with geocells at the embankment base can perform similarly to a geosynthetic reinforced piled embankment system, which is costlier but very efficient. When the modular ratio is more than 40, geocell-reinforced encased stone column-supported embankment is similar to GRPES.

The Analysis of a Proposed Experiment to Measure the Speed of Gravity in Short Distances

In order to investigate the speed of gravitational signals travelling in air or through a different medium two experiments were designed. One of the experiments contains 2 masses rotating at very high speed and in the other experiment a sapphire bar will vibrate, in both cases they will emit a periodic tidal gravitational signal and one sapphire device that behaves as a detector, which are suspended in vacuum and cooled down to 4.2 K will act as a detector. The vibrational amplitude of the sapphire detector device is measured by an microwave signal with ultralow phase-noise that uses resonance in the whispering gallery modes inside the detector device. Sapphire has a quite high mechanical Q and electrical Q which implies a very narrow detection band thus reducing the detection sensitivity. A new detector shape for the detector device is presented in this work, yielding a detection band of about half of the device vibrational frequency. With the aid of a Finite Element Program the normal mode frequencies of the detector can be calculated with high precision. The results show a similar expected sensitivity between the two experimental setup, but the experiment with the vibration masses is more stable in frequency then it is chosen for the experimental setup to measure the speed of gravity in short distances. Then a more precise analysis is made with this experiment reaching a signal-noise ratio of 10 at a frequency of 5000 Hz.

Effect of concreting pressure on ground response caused by installation of diaphragm wall panels

The ground response during diaphragm wall panel installation is strongly affected by the support slurry pressure, and by the subsequent lateral pressures during the tremie placement and set-up of wet concrete. The support slurry pressure can be reliably assumed as hydrostatic within the excavated trench, whereas the lateral concreting pressure is much more complex due to the stiffening effect of wet concrete. This paper reviews the measurements of wet concrete pressures from a series of instrumented diaphragm wall panels which show that lateral pressures in the concrete slurry increase as the tremie displaces bentonite slurry and reach a maximum condition about 1 h after placement, while conditions over the longer term closely approximate the hydrostatic pressure of the bentonite-filled trench. The maximum increase of pressure varies at different heights of the same trench, and also varies for two separate panels in the same project, reflecting the varying velocity of concreting. Model tests of concreting pressure on formwork also demonstrate that the lateral pressure reduces from hydrostatic wet concrete pressure a few hours after casting. A time-dependent lateral concreting pressure model is developed to represent these measurements more realistically. This proposed model is implemented into a finite-element program to investigate its effects on the ground response due to the concreting process. Computed results from a reference case can capture the progressive variations of ground movement, earth and pore water pressure in the soil adjacent to the trench during and shortly after the concreting process, which is consistent with the reported measurements.

Shear Strength of Nano Silica High-Strength Reinforced Concrete Beams.

In this study, the shear strength of sixteen full-scale over-reinforced concrete beams with and without nano silica (NS), constructed from high-strength concrete (HSC), was investigated both experimentally and analytically. Nano silica was used as a partial replacement for Portland cement. According to the NS ratio, the tested beams were divided into four groups: 0%, 1%, 2%, and 3%. Shear span to effective depth (a/d) ratios of 1.5 and 2.5 were used in each group, and two different stirrups ratios (ρv) were employed as 0% and 0.38%. The shear strength provisions used by some international codes, such as the American Concrete Institute (ACI-2019), the Eurocode 2 (EC-2), and the Egyptian Code (ECP 207), were examined when applied to HSC beams with and without NS. The most important factors to consider were the effect of using NS on the shear span to effective depth (a/d) ratio and the shear strength of the beams with and without stirrups. The experimental results were validated using a nonlinear finite element analysis using the computer program ABAQUS. The experimental results showed that increasing the NS ratio reduced the number of cracks, and increased the cracks spacing, as well as reducing crack width. In specimens without stirrups, these effects were more obvious. A rise in the (a/d) ratio increased the number of cracks along the beam length, notably in the mid-span region. For specimens without stirrups and with an (a/d) of 1.5, raising NS from 0% to 1%, 2%, and 3% increased the ultimate load by 13%, 30%, and 39%, respectively, whereas for specimens with an (a/d) of 2.5, the ultimate load increased with approximately the same increase as that in beams with an (a/d) of 1.5 due to using NS. Additionally, the addition of NS to concrete boosted the contribution of the concrete to the shear strength, as shown by the results of beams without stirrups. For specimens with stirrups and an (a/d) of 1.5, raising NS from 0% to 1%, 2%, and 3% increased the ultimate load by 8%, 21%, and 30%, respectively. Additionally, for specimens with stirrups and an (a/d) of 2.5, the ultimate load increased with approximately the same increase as that in beams with stirrups and an (a/d) of 1.5 due to using NS. The test findings indicate that the shear strength calculated using the equations of the ACI 318-19 is more conservative than EC-2 and ECP 207 for NS concrete beams. The finite element program ABAQUS may be successfully used to predict the shear strength of NS concrete beams.

Electromagnetic design and stress analysis of an 8 T no-insulation HTS insert coil for 20 T magnet

An 8 T no-insulation (NI) high temperature superconducting (HTS) insert has been designed using a 12 T low temperature superconducting (LTS) magnet to build a 20 T magnet. This paper focuses on the electromagnetic design and stress analysis of the 8 T HTS insert coil. The preserve elitist genetic algorithm was adopted to design a coil with the least cost in conjunction with the finite element program. The pre-stress during the winding, the thermal stress during the cooling down, and the electromagnetic stress considering screening current effect during the charging of the HTS insert coil were analyzed and discussed in this paper.

Simulation of hard rock pillar failure using 2D continuum-based Voronoi tessellated models: The case of Quirke Mine, Canada

The Quirke Mine, ON, Canada, is a typical example of a mine that experienced a chain reaction of pillar failure. In this mine, the rib pillars were initially laid out with their long axis parallel to the dip direction of the orebody. In the central part of the mine, the pillars were re-aligned at 45° to the orebody true dip. This realignment resulted in adverse shear loading conditions that led to their failure. In this study, a two-dimensional finite element program was used to simulate the failure of Quirke Mine pillars under compressive and shear loading conditions. The pillars were simulated as a heterogeneous material, consisting of randomly generated Voronoi blocks. The calibration of this model, referred to as a Voronoi Tessellated Model (VTM), was conducted against the rock mass strength estimated based on a tri-linear, brittle failure criterion. The calibrated VTM was then employed to investigate the pillar behavior during drift development and stope excavation. It was found that the pillar under shear loading experiences higher confinement loss and tensile stress at its core and, therefore, fails at a lower stress level than that under compression. The simulated pillar failure process was found to agree with documented field observations.

Thermo-electrical performance of hybrid busbars: An experimental and numerical investigation

This paper is focused on hybrid busbars made from aluminum and copper with the purpose of analyzing the influence of temperature on the electric performance of the joints. The methodology involves the fabrication of fastened, friction stir spot welded, sheet-bulk compressed, and injection lap riveted unit cells that are representative of the different types of hybrid busbars joints, the development of a special purpose laboratory apparatus for thermo-electrical measurements, and numerical simulation with a finite element computer program developed by the authors. Results are a step forward in understanding the variation of the electrical resistance of hybrid busbars with temperature and allow concluding that an increase above 30% is expected when the temperature in service reaches the limiting value defined by the IEEE standard for metal-clad switchgear.

Shaking table test and numerical simulation of shallow foundation structures in seasonal frozen soil regions

Frozen soil layers can induce the formation of double or multilayers on the ground. Such formations change the dynamic characteristics and dominant period of soil, directly influencing the stability and safety of upper buildings. In this paper, the frozen soil-structure interaction system in cold region was taken as the research object. The frozen soil model was made artificially, and two kinds of structure models with different natural frequencies were designed. Through a series of shaking table tests and finite element numerical analysis, the influence of structural natural frequency, soil frozen depth and seismic load on the seismic response of structure were studied. The test results indicate that ground freezing could weaken the soil–structure interaction effect and the nonlinear development of the soil structure. The effect of peak acceleration amplification of the ground is significant close to the surface. The acceleration amplification coefficient of the ground surface decreased as the freezing depth increased, which indicates that the freezing of the ground suppressed the acceleration response of the ground surface. If the peak frequency of a seismic wave is close to the natural frequency of the structure, it can significantly amplify the seismic response of the structure. Owing to the interaction between the soil and the structure, the degree of liquefaction of the ground varied with different structures. Subsequently, a nonlinear finite element program was used to establish the dynamic calculation model of frozen soil-structure interaction system considering the gradient change of stiffness of frozen soil and the dependence of frozen soil on temperature. On the basis of validating the numerical model rationality, the seismic response of frozen soil-structure interaction system under horizontal seismic excitation was further explored. The analysis results show that the seismic response of the structure increased significantly with amplitude excitation; the greater was the freezing depth, the greater was the seismic response of the structure, The influence of the frozen ground on the seismic response of structures in the design of structures in frozen soil areas should be considered. In summary, the dominant period of the ground, the dynamic characteristics of a structure, the type of seismic wave, and the degree of liquefaction of the ground have a significant influence on the seismic response of the structure. Therefore, considerable attention should be paid to the influence of frozen soil on the dynamic characteristics of a structure in frozen soil regions.

Novel bi-layer beam elements for elastic fracture analysis of delaminated composite beams

A general finite element method is proposed for linear elastic fracture analysis of delaminated bilayer composite beams. An interface deformable bilayer beam model is adopted in modeling the virgin portions of bilayer beams, and it is capable of guaranteeing the continuity condition of internal forces at the tip of delamination because the bilayers are modeled as two separate shear deformable sub-beams and both the interface normal and shear compliances are introduced to account for interface deformation. The stiffness matrices of bilayer beams using the linear and quadratic interpolation polynomials are both derived using the principle of minimum potential energy. Then, a finite element program is developed by assembling the element stiffness matrices of virgin and delaminated portions of bilayer beams and applying the corresponding equivalent nodal forces. Two typical fracture specimens (i.e., single leg bending and end-notched flexure bilayer beams) are analyzed using the proposed bilayer beam elements. The computed displacement and energy release rate are compared well with those of analytical solutions, and the mode components of energy release rate for single leg bending specimen are also obtained using the virtual crack closure technique. It demonstrates that the proposed novel bilayer beam elements are capable of effectively and efficiently predicting the displacement and energy release rate (including its mode components) of delaminated bilayer beams. The developed bilayer beam element is general in nature and accurate and efficient in particular, because it can achieve the same accuracy as the high order beam theory and be easily implemented in the existing commercial finite element software.

Behavior of Reinforced Concrete Deep Beams with Openings under Vertical Loads Using Strut and Tie Model

This research aims to study the effects of the size and location of openings on deep beams. The analysis of deep beams with openings presents a rather complex problem for engineers, as there are currently no guidelines within the design codes for this problem. Using the strut and tie model is a feasible solution, but also gives some uncertainties due to the various models that can be used. This paper proposes using a strut and tie model for the deep beams with openings where reinforcement is laid out in the form of embedded struts and ties. The study is divided into an experimental and a numerical part. The experimental study was conducted on eight reinforced concrete deep beams under vertical loads. Seven of the beams had web openings of different sizes and locations, while the eighth specimen was a reference beam without any openings. The beams had the same concrete dimensions with the size of the openings in the web taken as 150 150 mm and 300 300 mm, and the location of the opening in the horizontal direction was varied between 0.11 to 0.4 the span. The experimental results were analyzed in terms of cracking pattern, mode of failure, and load-deflection behavior and then compared to numerical analysis conducted using a finite element program. A parametric study followed to investigate the influence of reinforcement arrangement and reinforcement around the openings on the behavior of deep beams. The results showed that large web openings that directly interrupted the compression strut had the most reduction in beam capacity and that the location of the opening did not significantly affect the strength of the beam in the case of small openings. Doi: 10.28991/CEJ-SP2021-07-011 Full Text: PDF

A nonlinear visco-hyperelastic model for spray polyurea and applications

Spray polyurea (SPUA) is widely used as a protective coating material for engineering structures subjected to the intensive impulsive loadings attributed to its large deformation and viscoelastic properties. Both experimental and theoretical studies of the hyperelastic and viscoelastic behaviors of SPUA, as well as the applications in the numerical simulations of the SPUA retrofitted structures under impact and blast loadings were conducted. Firstly, the reasonable geometries and dimensions of specimens are designed, and the complete compressive stress-strain curves of SPUA with the strain rate ranging from 10−3-103 s−1 were experimentally derived. The dependences of the dynamic initial elastic modulus, stress and fracture strain on the strain rate are formulated. It indicates that the initial elastic modulus and stress increase as the strain rate increases, while the fracture strain is linearly negatively correlated with the logarithm of strain rates. Then, a twenty-four-parameter nonlinear visco-hyperelastic constitutive model composed of a hyperelastic model and seven Prony series terms is established and validated, in which the model parameters are determined through a multi-objective optimization based on genetic algorithm. Finally, by evaluating the existing sixteen constitutive models embedded in finite element program LS-DYNA, the Simplified rubber/foam model is selected for describing the mechanical behavior of SPUA. The Simplified rubber/foam model parameters are further calibrated by the established nonlinear visco-hyperelastic model and comprehensively validated by comparisons with six series of impact and explosion tests on the SPUA, SPUA retrofitted steel plate and masonry wall. The present work could provide a helpful reference for the design and evaluation of the SPUA retrofitted structures.

Numerical Simulation Analysis of the Seismic Performance of Precast Bridge Piers

Precast technology is increasingly favoured by bridge engineers, and the seismic performance of precast bridge piers urgently needs to be addressed. Precast piers have a complex load-bearing mechanism, and their design method has not been clearly determined. Fibre plastic hinge theory can satisfactorily analyse the seismic performance of precast piers. In this study, the seismic performance of precast piers is analysed through numerical simulation of pier columns based on the pseudostatic testing of a set of existing precast piers and combined with fibre plastic hinge theory. The results show the following: With reasonable constructional measures, precast piers connected by grouted sleeves indeed have seismic performance similar to that of cast-in-place components. Finite-element programs can be employed to simulate the mechanical properties of steel rebars before yielding well but not those after yielding or under fatigue. When fibre plastic hinges are used for finite-element analysis, if the fibre cross-section is reasonably divided, the length of the plastic hinge has little influence on the results; otherwise, too densely distributed plastic hinges may lead to nonconvergence of the results in a later working condition. The plastic hinge method recommended in this paper, especially the sectional fibre-cross-section division method, can obtain the plastic hinge performance state, it can help save the test cost and make up for the shortage of test data.

Damage Assessment of Simply Supported Double-Pier Bent Bridge under Heavy Truck Collision

Studying the failure or collapse mechanism of an entire bridge under vehicle–pier collision has engineering demand and practical meaning, while the existing damage assessment work mainly focuses on the impacted pier. This study aims to numerically clarify the collapse mechanism and evaluate the damage level of the entire bridge. First, the previously validated finite-element (FE) model of a simply supported RC bridge with double-pier bent when impacted head-on by a heavy truck. The model improved by incorporating the nonlinear behaviors and damage of the bridge superstructure. According to the truck mass and impact velocity involved in the actual collision accidents, 20 truck–pier collision scenarios are designed and numerically simulated by adopting the nonlinear FE program LS-DYNA. The damage/failure or collapse mechanism of the entire bridge, as well as the vehicular impact force and bridge structural dynamic behaviors, are examined. It shows that (i) the overall collapse of the bridge structure is an impact-successive and damage-accumulative process, which is not completely coincident with the failure of impacted pier; and (ii) the cargo-induced internal forces of the impacted pier have two peaks attributed to the initial contact and the following pushing–drag effect of cargo, respectively. Then, based on the damaged area of concrete and effective plastic strain of reinforcement, the damage levels of the main bridge components, including the pier, bent cap, tie beam, pile, girder, and deck, are qualitatively assessed and classified, followed by the clarifications of their corresponding inner correlations. Furthermore, by proposing two quantitative damage indexes, a feasible on-site approach for assessing the post-collision damage of the bridge structure is established and validated by eight additional collision scenarios, and the dependency of bridge damage level on both the vehicular impact velocity and mass is graphically presented. The proposed approach can be practically generalized to on-site damage evaluation of a bridge structure after actual accidents and can provide useful reference in design and restoration of RC bridges.

Sıvılaşan Zeminlerde Kazık Davranışına Dair Parametric Bir Çalışma

Liquefaction in saturated sandy soils under cyclical loads has a significant part in the structural damage cases. Pile foundations, used for soils with bearing capacity problems, might get exposed to various liquefaction-based damages. The finite element program FLAC2D is utilized to understand the pile behavior in liquefied soils under dynamic loads. The 1999 Kocaleli earthquake record was used in the numerical analysis for a single pile element in the layered soil profile with liquefied and non-liquefied soil. The pile-head of the model used in the layered soil sample was left free for rotation. Calculations for a single pile profile where axial load and horizontal load are affected simultaneously were performed by considering both the kinematic and inertial effect. Finite difference analyzes were performed by changing the embedded lengths of pile socket according to the existence and absence of a non-liquefying crust layer on the liquefied soil in the layered soil profile. As the results of the pile-head displacement and maximum moment value output were assessed.