Three-dimensional Finite Element Method Research Articles

Synergistic densification mechanism of irregular Ti powder during CIP: 3D MPFEM simulation with real-shape particles

Achieving high green density is essential for ensuring the mechanical properties of powder metallurgy workpieces. However, the densification behavior of irregular ductile powders remains unclear due to oversimplification in current numerical simulations. To address this, a three-dimensional multi-particle finite element method model incorporating realistic powder morphology, size distribution, and stacking structure is constructed. It is found that a pivotal motion-deformation synergistic stage exists between the conventional particle rearrangement and elastic–plastic deformation stages. In this stage, plastic deformation is driven by the spheroidization of coarse powders, whereas the resulting vacancies in the stacking structure facilitate slight particle motion. Thereafter, plastic deformation is dominated by the flattening of fine particles, and the pore-filling capacity decreases due to the reduction in non-contact surface area. This synergistic and complementary interaction between the spheroidization of coarse powders and the flattening of fine powders enhances mechanical interlocking and promotes micropore closure. As a result, the micropores exhibit a tendency of downsizing and homogenization, substantially boosting the potential for achieving full densification during sintering. Based on these findings, a method for determining the optimal forming pressure is proposed, considering the manufacturing costs of powder compacts and the characteristics of the micropores in both green and sintered bodies.

A comprehensive numerical procedure for high-intensity focused ultrasound ablation of breast tumour on an anatomically realistic breast phantom.

High-Intensity Focused Ultrasound (HIFU) as a promising and impactful modality for breast tumor ablation, entails the precise focalization of high-intensity ultrasonic waves onto the tumor site, culminating in the generation of extreme heat, thus ablation of malignant tissues. In this paper, a comprehensive three-dimensional (3D) Finite Element Method (FEM)-based numerical procedure is introduced, which provides exceptional capacity for simulating the intricate multiphysics phenomena associated with HIFU. Furthermore, the application of numerical procedures to an anatomically realistic breast phantom (ARBP) has not been explored before. The integrity of the present numerical procedure has been established through rigorous validation, incorporating comparative assessments with previous two-dimensional (2D) simulations and empirical data. For ARBP ablation, the administration of a 0.1 MPa pressure input pulse at a frequency of 1.5 MHz, sustained at the focal point for 10 seconds, manifests an ensuing temperature elevation to 80°C. It is noteworthy that, in contrast, the prior 2D simulation using a 2D phantom geometry reached just 72°C temperature under the identical treatment regimen, underscoring the insufficiency of 2D models, ascribed to their inherent limitations in spatially representing acoustic energy, which compromises their overall effectiveness. To underscore the versatility of this numerical platform, a simulation of a more clinically relevant HIFU therapy procedure has been conducted. This scenario involves the repositioning of the ultrasound focal point to three separate lesions, each spaced at 3 mm intervals, with ultrasound exposure durations of 6 seconds each and a 5-second interval for movement between focal points. This approach resulted in a more uniform high-temperature distribution at different areas of the tumour, leading to the ablation of almost all parts of the tumour, including its verges. In the end, the effects of different abnormal tissue shapes are investigated briefly as well. For solid mass tumors, 67.67% was successfully ablated with one lesion, while rim-enhancing tumors showed only 34.48% ablation and non-mass enhancement tumors exhibited 20.32% ablation, underscoring the need for multiple lesions and tailored treatment plans for more complex cases.

Discrete differential geometry-based model for nonlinear analysis of axisymmetric shells

In this paper, we propose a novel one-dimensional (1D) discrete differential geometry (DDG)-based numerical method for geometrically nonlinear mechanics analysis (e.g., buckling and snapping) of axisymmetric shell structures. Our numerical model leverages differential geometry principles to accurately capture the complex nonlinear deformation patterns exhibited by axisymmetric shells. By discretizing the axisymmetric shell into interconnected 1D elements along the meridional direction, the in-plane stretching and out-of-bending potentials are formulated based on the geometric principles of 1D nodes and edges under the Kirchhoff–Love hypothesis, and elastic force vector and associated Hessian matrix required by equations of motion are later derived based on symbolic calculation. Through extensive validation with available theoretical solutions and finite element method (FEM) simulations in literature, our model demonstrates high accuracy in predicting the nonlinear behavior of axisymmetric shells. Importantly, compared to the classical theoretical model and three-dimensional (3D) FEM simulation, our model is highly computationally efficient, making it suitable for large-scale real-time simulations of nonlinear problems of shell structures such as instability and snap-through phenomena. Moreover, our framework can easily incorporate complex loading conditions, e.g., boundary nonlinear contact and multi-physics actuation, which play an essential role in the use of engineering applications, such as soft robots and flexible devices. This study demonstrates that the simplicity and effectiveness of the 1D discrete differential geometry-based approach render it a powerful tool for engineers and researchers interested in nonlinear mechanics analysis of axisymmetric shells, with potential applications in various engineering fields.

Analyzing the effect of undermining on suture forces during simulated skin flap surgeries with a three-dimensional finite element method

Skin flaps are common procedures used by surgeons to cover an excised area during the reconstruction of a defect. It is often a challenging task for a surgeon to come up with the most optimal design for a patient. In this paper, we set up a simulation system based on the finite element method for one of the most common flap types — the rhomboid flap. Instead of using the standard 2D planar patch, we constructed a 3D patch with multiple layers. This allowed us to investigate the impact of different undermining areas and depths. We compared the suture forces for each case and identified vertices with the largest suture force. The shape of the final suture line is also visualized for each case, which is an important clue when deciding on the most optimal skin flap orientation according to medical textbooks. We found that under the optimal undermining setup, the maximum suture force is around 0.7 N for top of the undermined layer and 1.0 N for bottom of the undermined layer. When measuring difference in final suture line shape, the maximum normalized Hausdorff distance is 0.099, which suggests that different undermining region can have significant impact on the shape of the suture line, especially in the tail region. After analyzing the suture force plots, we provided recommendations on the most optimal undermining region for rhomboid flaps.

Three-dimensional simulation on phase change heat transfer of moving spherical particle

Investigating the motion process of paraffin particle under a mesoscopic scale is very helpful to master the heat transfer mechanism of the mushy zone in solid–liquid phase change. Prior researches predominantly focused on either particle motion or phase change, without accounting for their coupling. In this study, the three-dimensional finite element method is used to solve the motion and heat transfer of the particle, taking into account the coupling of motion and phase change. The moving grid is employed to trace the interface of moving particles and liquid using the Arbitrary Lagrangian-Euler method, which is able to calculate flow and heat transfer in fluid region and allow grid deformation in solid region. The results indicate that uneven fluid velocity around the particles results in non-uniform temperature gradients on particle’s surface. In areas with larger temperature gradient, it melts more quickly and its deformation is obvious. The maximum is located at particle orientation angle 30°. Changing the size and direction of fluid velocity will reinforce or inhibit the movement of particle. The changing time of motion direction when fluid velocity is −0.03 m/s shorten 2.7 times than when fluid velocity is −0.01 m/s. The initial temperature of the surrounding fluid has a positive relationship with the particle melting rate. The channel width affects significantly the motion and melting of particle. The initial position of particle has an important effect on it’s falling movement, and the closer is close to the wall of channel, the greater the displacement of left and right movement.

Integrating parametric HFGMC and isogeometric RZT[formula omitted] for multiscale damage modeling of composite structures: A numerical and experimental study

In this research effort, a novel multiscale analysis scheme is proposed for damage modeling of composite laminates, sandwich structures, and stiffened plates relying on capabilities of the parametric HFGMC and isogeometric RZT{3,2} formulations. The Ramberg Osgood (RO) model is incorporated into the micromechanics model to reflect polymer matrix material nonlinearities on the overall homogenized composite behavior. Carbon fibers are assumed to behave in a linear transversely isotropic manner. The higher order RZT{3,2} theory employed at the macro level facilitates efficient applicability of the model to thick composite laminates and soft core sandwiches. On the other hand, it generates all three-dimensional stress components and thus ensures dimensional consistency between micro and macro levels. Numerical discretization and prediction of RZT{3,2} kinematic variables are enabled by performing NURBS based isogeometric analysis (IGA) thereby enhancing modeling efficacy to a significant degree. Soft core plasticity and failure in the composite are evaluated at the macro level through the RO model and Hashin criteria, respectively. Applicability of the method is presented for thin and thick flat composite and sandwich laminates; and further extended to stiffened plates via developing a multipatch formulation. A comprehensive validation of our analysis is conducted by comparing the results with established benchmarks from the literature, experimental data, and three-dimensional finite element method (3D-FEM) simulations. Initially, a moderately thick, simply supported square laminate under transverse loading is examined, a common verification benchmark. Then, results from standard mechanical tests, including tensile, shear, and four-point bending tests on thin laminates, followed by experiments on moderately thick sandwich structures subjected to four-point bending, are presented. Finally, the analysis is extended to a stiffened plate under uniform pressure, demonstrating the method’s accuracy and applicability across diverse structural configurations.

Application of a Modified First-Order Plate Theory to Structural Analysis of Sensitive Elements in a Pyroelectric Detector.

Pyroelectric materials, with piezoelectricity and pyroelectricity, have been widely used in infrared thermal detectors. In this paper, a modified first-order plate theory is extended to analyze a pyroelectric sensitive element structure. The displacement, temperature, and electric potential expand along the thickness direction. The governing equation of the pyroelectric plate is built up. The potential distributions with upper and lower electrodes are obtained under different supported boundary conditions. The corresponding numerical results of electric potential are consistent with those obtained by the three-dimensional finite element method. Meanwhile, the theoretical results of electric potential are close to that of experiments. The influence of supported boundary conditions, piezoelectric effect, and plate thickness are analyzed. Numerical results show that the piezoelectric effect reduces the electric potential. The thickness of the pyroelectric plate enhances the electric potential but reduces the response speed of the detector. It is anticipated that the pyroelectric plate theory can provide a theoretical approach for the structural design of pyroelectric sensitive elements.

Case studies of the load-bearing performance of shield tunnel segment with misaligned defects

The segment misalignment is a common defect in the segment installation of a shield tunnel construction, due to the complexity and uncertainty of its construction conditions. This raises a concerning about the safety of the segment lining for the shield tunnel. In this paper, the integrated numerical models with surrounding rock, peastone grouting and segment lining were built using three-dimensional finite element method, by introducing two kinds of misaligned defects of segments. One was the misalignment that elongated the horizontal axis of the transversal ring section of segment lining, another was the misalignment between adjacent rings of segments. To eliminate the impact of boundary on numerical results, seven rings of segments are built for the three-dimensional finite element models, and the middle ring is dealt with for the results analysis under V-class surrounding rock, including the circumferential stress of outer and inner layers of the segment, the contact stress on joint surface between segments, and the stress of locating pins between adjacent rings. Results indicate that the two kinds of misaligned defects create pronounced impact on tensile stress of segment at the bottom and the crown segments, respectively, which produces a greater tensile stress to increase cracking risk even abrupt fracture of segment. However, the misaligned defects have a slight impact on the contact stress and the locating pins stress. Therefore, attention should be paid to the cracking of bottom or crown segments in the segment lining of shield tunnel.

Simulation study of a highly sensitive I-shaped Plasmonic nanosensor for sensing of biomolecules

This paper presents the design and simulation of an I-shaped metal insulator metal waveguide-based nanosensor for biosensing applications. The device’s sensing property is investigated using the three-dimensional finite element method. In the proposed design a I-shaped cavity is coupled to the main waveguide that serves as a resonator to generate the resonance peaks. The refractive index of the material to be sensed is filled inside the I-shaped cavity. This sensor operates in the near and mid-infrared wavelength ranges. The device can identify a variety of biomolecules, including cancer cells and bacterial samples. The simulation results reveal that device shows different resonance dips for different refractive indexes of cancer cells. The device can obtain sensitivity of 1550 nm RIU−1 and 1250 nm RIU−1 among refractive index of normal and cancerous cell for basal and hella cancer cells, respectively. Instead of all these biomolecules, the nanosensor shows different resonance dips in the transmittance spectrum for DNA, RNA, and ribonucleoprotein. Furthermore, the sensor has demonstrated potential applicability as an HB concentration detector and for sensing other blood components. Moreover, we improved the structure characteristics by varying the length and centre area of the cavity, demonstrating that modifying the device parameters can boost sensitivity. After making structural adjustments to the device, the maximum sensitivity of 3000 nm RIU−1 is achieved for some bacterial samples.

Nonlinear Analysis of Electric Potential in a Piezoelectric Thin Plate as Pressure Sensor

Piezoelectric materials are widely applied in electronic components due to their ability to couple electric and mechanical fields. For the piezoelectric thin plate as a pressure sensor, we extend the modified first-order piezoelectric plate theory to explore the nonlinear solution of electric potential and discuss the relevant regulation mechanisms. Based on the piezoelectric effect, the electric potential generated by deformation is not linear with thickness. A quadratic function of electric potential across thickness is introduced. However, the electric potential on upper and lower electrodes is an unknown constant, which can be determined by the nonlinear complementary equation based on the Gauss theorem. It is shown that the nonlinear results of electric potential are consistent with outcomes by the three-dimensional finite element method. Furthermore, relevant regulation mechanisms are discussed on electric potential, including supported conditions, plate thickness, and load area. In addition, the influence of load locations on the electric potential response is analyzed. It is expected that these findings will be instructive to the structural design of piezoelectric pressure sensors.

Design and optimization of microchannel for enhancement of the intensity of induced signal in particle/cell impedance measurement.

The measured impedance signal of a single particle or cell in a microchannel is of the μA level, which is a challenge for measuring such weak signals. Therefore, it is necessary to improve the intensity for expanding the applications of impedance measurement. In this paper, we analyzed the impact of geometric parameters of microchannel on output signal intensity by using the three-dimensional finite element method. In comparison to conventional microchannels, which are distributed at a uniform height, the microchannels in this design use the height difference to enhance the signal intensity. By analyzing the effects of the geometric dimensions of the constriction channel, main channel height, radius of particles, types of cells, shapes of particles with different ellipticities, and particles spacing on the current signal, we concluded the optimal dimensions of these parameters to improve the intensity of the induced current signal. Through the fabrication of the optimized size of device and experimental demonstration, it is verified that the current signal intensity caused by the particle with a diameter of 10 µm is nearly twice that of the conventional structure with a height of 20 µm, which proves the correctness of the optimization results and the feasibility of this work. In addition, the performance of the device was verified by measuring the mixtures of different size particles as well as non-viable and viable yeast cells.

Influence of a waveform on the bit–rock impact response considering reflected waves in a drill rod

Percussive drilling is considered an efficient approach for penetrating hard formations. Understanding the responses and mechanical properties of rocks while being impacted and crushed by rock drills is essential for further improving their penetration efficiencies. This paper examines the consecutive impacts between the drill bit and rock, which are induced by the waves reflected in the drill rod after an initial hammer impact. Firstly, the loading and unloading principle for consecutive impacts is proposed. Based on this principle and one-dimensional (1-D) longitudinal wave propagation, a 1-D bit-rock interaction dynamics model is subsequently established. This model considers switches between the states of impact and separation, to instantly predict rock responses. Selecting marble as a representative material, the findings from the 1-D theoretical model and three-dimensional (3-D) Finite Element Method (FEM) simulations indicate that the number of repeated crushing impacts, which substantially contribute to the final penetration displacement, increases as the wavelength or the baseline level of fc (dimensionless crushing threshold force) in a rock decreases. fc is related to the loading rate, and its baseline level diminishes with decreasing impact energy (waveform amplitude). Due to the increases in fc and loading stiffness for short waves, the overall increasing trend of the final penetration displacement with decreasing wavelength weakens. A suitably-short wave with a high dimensionless exponential growth rate r or a long wave with approximately a unit of r can lead to a relatively-high final penetration displacement. In addition, we find that the dynamic loading and unloading stiffness and crushing threshold force have specific relationships with the penetration displacement and rock loading rate.

Comparative Study of High-speed Permanent Magnet Synchronous Motors with In-line Slot Conductors and Equidirectional Toroidal Windings

The high-speed permanent magnet synchronous motor (HSPMSM) plays an important role in a wide range of engineering fields due to its high power density, high efficiency, and light weight. In this paper, a HSPMSM equipped with in-line slot conductors(I-LSC) is proposed and compared with one equipped with equidirectional toroidal winding (ETW). Firstly, the differences between them are revealed, including topology, back-electromotive force (EMF), slot fill factor, copper loss, and torque. Secondly, two-dimensional finite element method (2D-FEM) tools are used to obtain more precise performance such as air-gap field, back-EMF, torque characteristics, efficiency maps, and the unbalanced magnetic force (UMF). Considering the end-windings of copper loss of ETW and the end ring copper loss of I-LSC, the losses and efficiency of two motors are simulated by three-dimensional finite element method (3D-FEM). Finally, the simulation results validate the feasibility of the newly proposed winding and indicate that in-line slot conductors have superiority in power density due to the high slot fill factor.

Theoretical analysis on the behavior of SPM anchor piles embedded in sand under oblique pullout load with emphasis on the padeye depth

Single-point mooring (SPM) system has been used in offshore engineering for its superiority in overcoming severe sea conditions. However, researches focused on the interaction mechanism between the anchor pile and soil in SPM systems remains insufficient, especially regarding the calculation method for oblique pullout bearing capacity that considers padeye depth. Based on the p-y curve method and load transfer method, this paper presents a simple prediction method for the behavior of anchor piles embedded in sand under oblique pullout load. The theoretical predictions are validated through comparing with results from the three-dimensional finite element method and existing centrifuge model tests. The effect of the loading angle and the padeye depth are analyzed and discussed. A negative bending moment peak and axial force discontinuity phenomenon appear at the padeye depth. The optimal padeye depth for anchor piles in this study ranges from approximately 0.53 to 0.80 times the pile length. When the padeye depth is less than 0.33 times of the pile length, the ultimate bearing capacity of the anchor pile increases with increasing load angles. Conversely, when the padeye depth exceeds 0.33 times the pile length, the ultimate bearing capacity decreases with the increasing load angles.

The study of the influence of the geometry of a lateral electric field resonator on its resonant characteristics

An experimental study of the dependence of the electrical impedance of a lateral electric field resonator on its thickness and the size of the gap between the electrodes was carried out. The resonator was made of PZT-19 piezoceramics in the form of a rectangular parallelepiped with the shear dimensions of 18 × 20 mm2. Two rectangular electrodes with a gap that varied in the range from 4 to 14 mm were applied on one side of the resonator. For each gap width, the frequency dependences of the real and imaginary parts of the electrical impedance were measured using an impedance analyzer. It has been found that increasing the gap width leads to an increase in the resonant frequency and to an increase in the maximum value of the real part of the impedance. Three series of such experiments were carried out for three values of the resonator thickness: 3.02, 2.38 and 1.9 mm. The resonant characteristics of the resonator were also theoretically analyzed by finite element analysis using two models. One resonator model was based on a two-dimensional finite element method. In this case, the vibration modes that existed due to the finite size of the plate in the direction parallel to the gap between the electrodes were not taken into account. The second model of the resonator used a three-dimensional finite element method, which correctly took into account all vibration modes existing in the resonator. Comparison of theory with experiment has shown that the three-dimensional model provides a better agreement between theoretical and experimental results.

Modeling of contact resistivity and simplification of 3D homogenization strategy for the H formulation

The finite element method (FEM) provides a powerful support for the calculations of superconducting electromagnetic responses. It enables the analysis of large-scale high-temperature superconducting (HTS) systems by the popular H formulation. Nonetheless, modeling of contact resistivity in three-dimensional (3D) FEM is still a matter of interest. The difficulty stems from the large aspect ratio of the contact layer in numerical modeling. Nowadays, an available solution is to model the contact layer with zero thickness but requires the discontinuity conditions of the magnetic field. In this paper, the energy variational method is utilized to incorporate the contribution of contact resistivity into the H formulation. From the perspective of energy transfer, the contact resistivity is related to the energy dissipation of the radial current flowing through the contact interface. In terms of applications, this method can be employed to calculate the charging delay of no-insulation coils and the current sharing behaviors of CORC cables. One advantage of this model is that the magnetic field is continuous and hence can be easily implemented in FEM. Additionally, it requires fewer degrees of freedom and hence presents advantages in computational efficiency. Moreover, this method can be employed to simplify the 3D H homogeneous model for insulated coils. The above discussions demonstrate that the proposed model is a promising tool for the modeling of contact resistivity.

Development of novel artificial intelligence functions based on 3D finite element method using February 6 Kahramanmaraş Seismic Records for earthquake effects prediction in various soils

The seismic events on February 6, 2023, in the province of Kahramanmaraş/Türkiye, caused severe damage and the collapse of numerous structures due to underlying soil issues. This catastrophe revealed the inevitable requirement to evaluate the effect of soil profile on structural safety. In the present study, novel artificial intelligence (AI) functions based on the three-dimensional finite element (3D FE) method considering various soil parameters were developed to predict the effects of earthquakes. A 3D FE model of the ten-story building with a known soil profile and structural elements was created in the first stage, accounting for the soil-pile-structure interaction. After model validation, numerous parametric time history earthquake analyses were performed using the February 6 Pazarcık/Kahramanmaraş (Mw = 7.7) earthquake records. Therefore, the effects of soil parameters on acceleration, settlement, and lateral deformations were investigated. An innovative coding infrastructure, leveraging the power of AI, was developed to generate optimal network solutions automatically for creating high-order regression prediction functions. The 3D FE data was integrated into the code, and subsequently, an artificial neural network was utilized to formulate a function that yielded statistically significant outcomes. The created function accurately predicted the accelerations, settlements, and deformations. A novel method for indicating the potential deformations and accelerations inflicted by earthquakes based on soil parameters was introduced. This methodology can serve as a practical guide for researchers and project implementers in the initial design phases.

Research on the Correction of Soil Pressure Distribution Pattern in Circular Working Wells in Soft Soil Areas

This paper investigates the distribution characteristics of earth pressure on circular caisson foundations in soft soil areas based on practical engineering considerations. Utilizing a three-dimensional numerical analysis model and a displacement-based method for earth pressure calculation, the lateral earth pressure on the retaining structure is examined. Adjustments are made to the distribution pattern of earth pressure on circular caisson foundations in soft soil areas. The study demonstrates that the radius of the caisson significantly influences the spatial distribution of soil pressure. Additionally, empirical formulas for the depth and radius of the reduction in soil pressure around circular caisson foundations are obtained through the research. Comparative analysis reveals that the modified earth pressure planar foundation beam method, which accounts for the arching effect, is simpler, features more mature parameter selection, and is more cost-effective than the three-dimensional finite element method. In comparison to the standard planar elastic foundation beam method for earth pressure, it aligns more closely with the actual direction of displacement.

Size dependent scaling law of plastic flow in FCC nanolattices: A dislocation dynamics study

Micro- and nanolattices can achieve simultaneously both lightweight and ultra-high strength due to a combination of resilient architecture and enhanced mechanical properties of small-scale unit constituents. However, understanding the fundamental deformation mechanism for these novel materials remains intriguing due to the intricate interplay of various geometric characteristics and intrinsic microscopic defects. Here, we investigate the fundamental mechanism of plastic deformation in terms of dynamic evolution of defects and corresponding mechanical responses in aluminum nanolattices using a mesoscale defect dynamics model which couples three-dimensional dislocation dynamics and finite element method. Our concurrently coupled model could capture detailed dislocation motion under complex loading conditions and predict the plastic flow stress of the nanolattices. We demonstrate that the size of individual constituent beam plays a critical role in the properties of nanolattices through small-scale strengthening, showing the strength of the nanolattices increases with decreasing beam size with the scaling law of σ∝db−0.89. As a result, the scaling law of plastic yielding with material density drastically increases from the continuum prediction. In addition, our modeling could allow us to study the geometric effect with various nanolattices. These findings establish a foundation for the fundamental understanding of the governing mechanism of plastic deformation, allowing access to a new regime in designing optimal structures using nanolattices.

Influence of Subsoil and Building Material Properties on Mine-Induced Soil–Structure Interaction Effect

Soil–structure interaction (SSI) refers to the dynamic interaction between a structure and the surrounding soil on which it rests. The behavior of the soil can significantly affect the response of the building structure. In the context of civil engineering and structural analysis, SSI becomes particularly important when considering the response of structures to dynamic loads such as earthquakes or so-called paraseismic loads, e.g., mining tremors. Several factors contribute to SSI. Soil and building structure material properties, foundation type, and loading conditions are the most important parameters. The article concerns SSI in the case of mining rock bursts in Poland. The influence of changes in site material conditions and building material properties on the SSI phenomenon was investigated. A few variants of different properties of typical construction materials (brick, reinforced concrete, and cellular concrete) in the case of selected representative building structure were considered. The subsoil material properties from the wide range were also taken into account. Numerical three-dimensional finite element method (FEM) analysis was applied. The adopted models of the soil-structure system were verified by data from in situ experimental vibration measurements. A significant influence of the subgrade material and the building structure material on the SSI was demonstrated.