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Effect of Embedment Depth for Circular Footing on the Amplitude of Displacement under Dynamic Load

The effect of the embedment depth of a circular footing resting on dry sand and subjected to dynamic load on the amplitude of soil displacement (Az) was investigated the present study. In order to simulate the conditions occurring in the field, a special testing apparatus with accessories was designed and manufactured to study the effect of dynamic load on soil. A total of 18 cases were examined to take into account the effects of different parameters, including different frequencies (0.5, 1, and 2 Hz); relative densities (medium sand, R.D=50% and dense sand, R.D=80%); and corresponding unit weights (17.52 kN and 18.33 kN). All tests were carried out under load amplitude of 0.5 tons. The behaviour of the soil underneath the footing was examined by measuring the amplitude of displacement AZ using a vibration meter placed at a set depth (B) under the footing. It was found that when the embedment depth is changed from zero (at surface) to 0.5 B and then to B the value of amplitude of the displacement Az is reduced. The percentage of reduction in Az was about 4 to 39 % at depth 0.5 B, and about 37-77 % at depth B.


Introduction
The response of soil under dynamic loads usually differs from that under constant static loads, a fact of great significance for the constancy of structures. The behaviour of soil strain can be described as hysteretic and highly non-linear, and the actual behaviour of soils is normally elasto-plastic, which provides better estimations of displacement when  accelerations. The study concluded that increasing the footing embedment depth increases the amplitude of the force-time history by about 10 to30% due to increases in the degree of confinement. This is accompanied by a decrease in the displacement response of the soil of about 40 to 50% due to increases in the overburden pressure when the embedment depth increases, which leads to increases in the stiffness of sandy soil. There is also increase in the natural frequency of the soil-foundation system by about 20 to 45%. For surface foundations, the foundation is free to oscillate in vertical, horizontal, and rocking modes; however, embedding the footing causes the surrounding soil to restrict oscillation due to confinement which leads to an increase in the natural frequency. Moreover, Ali et al., (2018) found that the soil density increased with depth because of compaction, which makes the soil behave as if it were a solid medium. Increasing the footing embedment depth thus increases the damping ratio by 50 to 150% due to the increase in soil density as D/B increases, which causes the soil to tend to behave as a solid medium, activating both viscous and strain damping Das., (1983).

Research Methodology
The present work aimed to study the behavior of machine foundations resting on sandy soil subjected to vibration dynamic loadings. This research was carried out by considering a circular footing with diameter 150 mm placed on dry sandy soil. The boundary of the problem was achieved experimentally by using non-reflecting boundary materials (styropor cork). The variables taken into considerations were: 1. The depth of embedment of footing studied by placing the footing at the surface, then 0.5B and B below the soil surface.

3.
The effect of relative density of the sand, studied by resting the foundations on sand in a medium state (Dr = 50 %) and a very dense state (Dr = 80%).
For all parameters, the response of the soil-foundation system was evaluated by means of the following measurements:

Experimental Work and Material Used
Several methods are available to determine the displacement amplitude of machine foundations. Most of these methods consider the underlying soil as being in a medium state, however Al Mosawe et al., (2015). Small-scale experiments were thus performed to simulate a physical model of machine foundation on two types of soil so that the total numbers of tests was 18.
The physical characteristics for sand categorised as poorly graded (SP) with the Unified Soil Classification System (USCS). Table 1 summarises the properties of the sand used, and Fig. 1 shows the curve of the grain size distribution.
Testing was conducted in a steel cubical tank of dimensions 800×800×1000 mm with walls of 6 mm thickness, slicked on both faces, used to hold the soil. These measurements were selected to replicate the boundary influences of physical models exposed to dynamic loading. To ensure the uniformity through the model depth, 100 mm thick layers of soil were placed layer by layer and compacted manually to the marked level.
In order to simulate conditions in the field as closely as possible a specific investigating device with accessories was designed and manufactured to study the effect of machine vibration on soil. The loading system was a hydraulically mounted enhancement of the solid structure of the apparatus that was able to bear sufficient new loading amplitude as presented in Figure. 2.
The device was created from the following parts: 1-Loading frame.  A vibration meter was used to measure large movements in three directions (x, y, and z).

5-Data logging and acquisition systems.
The vibration device included an ADXL345 type accelerometer that is a little small power 3-axis accelerometer with sign condition electrical energy output as shown in Figure 3.

Effect of embedment depth on amplitude of displacement
The resulting amplitudes of displacement (AZ) for the vibrating foundation in medium and dense sand is given in Figures 6 to 11

Conclusions
1-In general, as the frequency increases, the strain decreases under identical load amplitudes and relatives sand density. The increment in strain reaches approximately 40% as the frequency changes from 2 Hz to 1 Hz, while the increment is approximately 60% when the frequency changes from 1 Hz to 0.5 Hz. This means that the strain increases as the frequency decreases.

2-
As the relative density of sand decreases, the strain increases under identical loads amplitudes and frequencies. The amplitude of displacement also increases under the same load amplitude and frequency, with the rate change increasing about 8% for frequencies of 0.5 Hz, and about 12.5% for 1 Hz and 20% for 2 Hz.