Numerical analysis of a concrete foundation under a combination of a dynamic and a seismic load

Improving in assembling technology has provided machines of higher evaluation with better resistances and managed behavior. This machinery led to remarkably higher dynamic forces and therefore higher stresses. In this paper, a dynamic investigation of rectangular machine diesel and gas engines foundation at the top surface of one-layer dry sand with various states (i.e., loose, medium and dense) was carried out. The dynamic investigation is performed numerically by utilizing limited component programming, PLAXIS 3D. The soil is accepted as flexible totally plastic material submits to Mohr-Coulomb yield basis. A harmonic load is applied at the foundation with amplitude of 10 kPa at a frequency of (10, 15 and 20) HZ and seismic load is applied with acceleration – time input of earthquake hit Halabjah city north of Iraq. A parametric statement is completed to evaluate the effect of changing the relative density, embedded depth and frequency of the machine. It has been noticed that the relative density plays an important role in the resistance of settlement, as it increases the resistance of the soil to the applied loads because the dense soil is stiffer. While total stress and displacement of different relative density decrease at the time when increasing the foundations' embedding, the ratio was (15%) at the depths (Df=0 and Df=2). In addition, it has been noticed that there decrease of displacement when the frequency value changes from (10 to 20) Hz.


INTRODUCTION
The analysis and design of the machine foundation require more consideration since it involves not only the static loads but also the dynamic loads caused by the machine's working. The fundamental objective in the design of a machine foundation is to confine the movement amplitude, which will endanger the satisfactory action of the machine. Various techniques have been created throughout the years to calculate the dynamic reaction of the soil-foundation system. The way to deal with such issuing is to register the matrix of dynamic impedance functions, which relate consistent state force and displacement at the foundation soil system.

Research Background:
The machine foundations should be designed such that the dynamic forces of machines are transmitted to the soil through the foundation so that all kinds of harmful effects are eliminated (Piyush K. Bhandari, Ayan Sengupta 2014). The presentation is focused on the parameters that have been studied in this research. The most important parameters that were illustrated are relative density, embedded depth, frequency of the machine, and behavior of sandy soil under the effect of dynamic loads. The arrangements are acquired by utilizing a three-dimensional finite element method by calculating the values of total stress and displacement under a combination of a dynamic and a seismic load.

Research Signification:
The soil response under dynamic loads is different from that of static loads because it is of significant importance for the stability of structures. Exhibited to dynamic loads, which depends on the speed of the machine and natural frequency of the foundation and the level of stress that cause dynamic strains as well as the type of the soil. Thus, a vibration analysis becomes necessary; therefore, the complete knowledge of the load-transfer mechanism from the machine to the foundation and the complete knowledge of excitation forces and associated frequencies are a must for the correct evaluation of machine performance.

Literature Review:
(Kaream et al., 2020) conducted experimental work to study the effect of the machine's circular foundation on the variation of surface settlement, vertical displacement, and stress with several cycles. Six laboratory model footings were prepared on medium and dense dry sand separately. A circular steel model of (150 mm) diameter was used to represent the footing. The models were tested under dynamic load amplitude of 0.25 ton and different frequencies of 0.5, 1, and 2 Hz. It was found that the rate of increase in settlement decreased remarkably when increasing the frequency for both types of sand. (Hadi and Al-Helo, 2015) carried out a dynamic analysis of strip machine foundation to evaluate the dependency of machine foundation on the modular ratio of soil layers of two-layer saturated sand with different states. The dynamic analysis is performed numerically by using finite element software, PLAXIS 2D. A harmonic load is applied at the foundation with an amplitude of 25 kPa at a frequency of 5 Hz. It was concluded that the displacement decreased remarkably when E1is duplicated 2-4 times E2. The pore water pressure increases remarkably when E1 is increased to about five times E2, then the effect decreases. (Al-Azawi et al., 2006) carried out a dynamic analysis of machine foundations under vertical excitations. The effect of embedment and foundation geometry was taken into account. The effect of embedment upon vertical forced vibration of a rigid footing was investigated theoretically. It was found that the embedment of foundations has a significant effect on the dynamic response. It causes an increase in the dynamic stiffness and damping coefficients and leads to an increase in the resonant frequency and a decrease in the dynamic response of the foundation. A convergence in results was obvious when the depth ratio was about 0.50. (Boumekik et al., 2010) presented laboratory tests for estimating the dynamic stress of the soil by a ''vibrating foundation prototype for three specific points of the foundation-soil interface zone''. A significant increase in the relative density of the medium dense sand was observed because of the particles' retightening in the central zone level, which increases their compactness. (Abd Al-Kaream, 2013) conducted experimental work to study the effect of vertical vibration of a machine on the response of saturated sand prepared at three relative densities (35, 60, and 80%). The type of dynamic load was cyclic of amplitudes 0.4, 0.6, and 0.8 kN and with frequencies of 0.16, 0.5, 1.0, and 2.0 Hz. It was found that the excess pore water pressure increases with increasing load amplitude, frequency, and relative density.

Research Gap:
Most of the researches focused on the dynamic load due to earthquakes and offshore waves. However, very little information was available about the effect of machine vibration on the performance of machine foundations with earthquakes and the soil underneath. Nowadays, the development in the industry has introduced huge machines that have a significant influence on the performance of the foundation and the soil underneath, producing is another type of vibration load. All machine foundations, irrespective of the size and type of machine, should be regarded as engineering problems, and their designs should be based on sound engineering practices.

Research Objective:
This study's main objective is to evaluate the behavior of the machine foundation under earthquake excitation by numerical analysis through the three-dimension finite element method with PLAXIS 3D MANUAL (2020). Also, studying the influences of dynamic loading variables (loading frequency, amplitudes) and relative density of machine foundation. Then, investigate the influences of parameters on the strain, amplitude displacement, and stresses in soils at various embedded depths for foundations on sand. Study the effect of the earthquake on the mentioned above properties compared to the effect of machine vibration.

Type of Machines:
According to frequency: (Srinivasulu and Vaidyanathan, 1990) Figure 1. Types of the machine according to the operating frequency.

ANALYSIS METHODS:
There are many analysis methods, but the finite element method (FEM) is the most commonly accepted analysis tool for solving engineering problems. It is used to solve simple and complex physical problems.
 The Linear Elastic Spring Method  The Elastic Half-Space Analogs Theory  The Impedance Function Method  Lumped Mass-Parameters System Method  Finite Element Method Low to the medium frequency of (0-8.32 HZ) like reciprocating machines Medium to the high frequency of (5-18 Hz) like diesel and gas engines Very high frequency of (16 -200 Hz) like electric motors and turbo generators Table 1. Parameters used for the numerical calculation.

Validation Model:
The verification was performed to check the accuracy of the PLAXIS by comparison with numerical and experimental studies to use it in analyzing Dynamic Behavior of Machine Foundations under Seismic Loadings excitation. Two cases were examined; the first examined the reliability of soil shear strength parameters using a suitable laboratory model. The second model was with free vibration and earthquake analysis of a building.

The Reliability of Soil Shear Strength Using a Suitable Laboratory Model:
The experimental work included subjecting the laboratory model to a series of tests to investigate the conduct of soil subjected to dynamic loading and the shear strength after a number of cycles. Footings of four shapes, circular with a diameter (150 mm), rectangular with dimensions of (300x100 mm), made of (20 mm) thick steel plates, were used. The test results revealed that Young's modulus of the steel used was 37.26 and 140.00 for secant and tangent modulus, respectively. In addition, the unit weight of the steel used was about 77.6 / 3 (Abdul-Kaream, 2020). This example demonstrates the natural frequency of a long five-story building when subjected to free vibration and earthquake loading. The building consists of 5 floors and a basement. It is 10 m wide and 17 m high, including the basement. The total height from the ground level is 5 x 3 m, and the basement is 2 m deep. A value of 5 2 is taken as the weight of the floors and the walls.
The building is constructed on a clay layer of 15 m depth underlayer by a deep sand layer. In the model, 25 m of the sand layer will be considered PLAXIS 3D MANUAL (2020).

Computational Model:
Dynamic

Results of Laboratory Model:
The numerical analysis of the selected case (the reliability of soil shear strength parameters) using PLAXIS 3D 2013 involved investigation of the strain the occurred due to vibration of machine with different the shape of foundation, by comparing the results of the numerical analysis with the experimental work, it appeared that the difference between the strain for the L/B ratio 3 are 10%, as shown in the Fig. 6A.

Influence of the Relative Density
Displacement in Z and X-direction: The vertical and horizontal vibration applied are estimated at the top main point. The illustrated Fig. 7 and Fig. 8 show the displacement reading versus the time of different relative density using soil with one layer (dense, medium, and loose sand) with operating frequency (20HZ). It has been noticed that the relative density plays an important role in the resistance of settlement, as it increases the resistance of the soil to the applied loads (Al-Ameri, 2014), so that the comparison shows that the value of vertical displacement decreases about 50% when increasing the value of the relative density by 80% as the dense soil is stiffer (Mitchell and Soga, 2005). The results presented a clear effect of the earthquake on the displacement compared with the effect of machine vibrations. The vertical displacement is enlarged by about 99% when an earthquake is influencing the machine foundation (Dr=40%). On the other hand, it was also being noticed from Fig. 8 that the horizontal displacement of loose sand is more (10-16) % when compared to medium and dense sand. The reason for this is due to an increase in the characteristics of dense and medium sand and a decrease in voids.

Total stress in Z and X-direction:
The numerical analysis shows the relationship between the total dynamic stress and the time in Fig. 9 to Fig. 11. It was noticed that the total dynamic stress in the dense sand was less than that of loose sand. These results confirm the findings of (Boumekik et al., 2010). Thus, the rise in the thickness of medium-dense sand due to the inhibition of particles at the level of the central region creates an increase in their density. On account of dense sand, the high axial pressure will have the direction to be moved to the corners because of the underlying confinement. In addition, Fig. 9 shows horizontal stress applied is measured at the top central point. It is clear that the behavior of the horizontal stress is slightly turbulent, as it records its highest value over a certain range of penetration when the soil is loose (550kPa) compared to dense sand (380kPa) that has a higher relative density and modulus of elasticity that led to disperse the generated stress, unlike loose soil that is easy to penetrate. On the other hand, from Fig. 12 and Fig. 13, which describe the vertical stress, it was be noticed that there is a relationship between the applied stresses and relative density, which can be taken into account that in dense soils and due to their properties, an increase in the applied loads occurs. Hence, the value of the stress increases with the stability of the area when compared with loose. In contrast, the highest value of stress in dense soils was (1,333) kPa, while in loose soils, it was about (1,121) kPa.

Displacement in Z and X-direction:
For a safe design of machine foundation, it must have the ability to resist dynamic loads; this subject has taken considerable attention in recent years. Embedment has a significant effect on the foundation's response and must be careful when evaluated (Hanash et al., 2020). The effect of three different embedded depths (at the surface, Df=1, and Df=2) has also been studied. Fig. 14 shows the vertical displacement amplitude in dense sand, and Fig. 15 draws horizontal displacement for dense sand. It was noticed that the displacement at depths (Df=1 and Df=2) was lower than that at the surface. The ratio was (15%) at the depths (Df=0 and Df=2) to dense sand. This implies that the insertion depth caused a meaning in the amplitude displacement among surface and insertion cases because of the increment in damping brought about by the soil-based foundation alongside the preparation for the soil-structure interaction (

Total stress in X and Z direction:
The process of including the foundation is of great importance in describing the stress curve, so it can be seen in Fig. 16, which hones of values of stress a point for at the surface of the soil that the foundation when it is at a surface, (i.e., Df = 0) and the point at the base of the foundation, the stress is a large amount compared to the foundation with (Df=2) where the point, in this case, becomes at the surface of the foundation, so it is far from the stress area, as shown in Fig. 17 -20 for a slice representing a section of the foundation, where the highest stress value at the apparent foundation is (1,333) kPa. The fully submerged It is (1,300) kPa in the vertical direction. As for the horizontal direction, it is (380) kPa for the (Df=0) and (370) kPa for (Df=2).

Influence of the Frequency of Machine for Medium Sand
Displacement in X and Z-direction: Fig. 21 and 22 show the relationship between the operating frequency (f˳) and the medium sand's total vertical and horizontal displacement. It has been noticed that when the frequency increases (10HZ) to (20HZ), a decline in the total vertical displacement occurs with (6.5%). In contrast, the effect is less in the horizontal displacement values than in the vertical displacement. Such behavior closely agrees with the conclusions made by

CONCLUSIONS
From the parametric review that was carried out in this research using the finite element program (PLAXIS 3D 2020) to analyze the foundations of the machine under seismic load placed on sandy soils of different relative densities and frequencies for a rectangular foundation, it can be drawn following: i. Three-dimensional analysis using the finite element method can be used to analyze the foundations of the machine under the seismic load on the soil in a successful way. ii. It has been noticed that a decrease in the vertical displacements by about 6.5% when changing the frequency of the machine from 10 to 15 Hz. In contrast, it was found that this effect is less for the horizontal displacement, which is clear from the results that the displacement curve with time can be described as sharp. iii. By studying the effect of the embedding depth on the vertical and horizontal displacements, it was found that when the embedding depth increases, the vertical and horizontal displacements decrease by 15%, and the value of vertical and horizontal stress decreases in proportions that vary according to the point chosen. iv.
The ratio between displacement caused by the earthquake and displacement caused by the vibration of the machine is 99%. v. The most significant variable influencing the issue of machine foundations is the relative density of the soil. It was discovered that by the exact technique, the greatest vertical displacement diminishes by half when the relative density increments as the kind of soil are sandy.